# Chapter 2 Motion Along a Straight Line Position, Displacement ... Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Essential idea: One of the earliest uses for electricity was to produce light and heat. This technology continues to have a major impact on the lives of people around the world. Nature of science: Although Ohm and Barlow published their findings on the nature of electric current around the same time, little credence was given to Ohm. Barlows incorrect law was not initially criticized or investigated. This is a reflection of the nature of academia of the time with physics in Germany being largely non-mathematical and Barlow held in high respect in England. It indicates the need for the publication and peer review of research findings in recognized scientific journals. Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents

Understandings: Circuit diagrams Kirchhoffs circuit laws Heating effect of current and its consequences Resistance expressed as R = V / I Ohms law Resistivity R = L / A Power dissipation Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Applications and skills: Drawing and interpreting circuit diagrams Identifying ohmic and non-ohmic conductors through a consideration of the V / I characteristic graph Solving problems involving potential difference, current, charge, Kirchhoffs circuit laws, power, resistance and resistivity Investigating combinations of resistors in parallel and

series circuits Describing ideal and non-ideal ammeters and voltmeters Describing practical uses of potential divider circuits, including the advantages of a potential divider over a series resistor in controlling a simple circuit Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Applications and skills: Investigating one or more of the factors that affect resistivity experimentally Guidance: The filament lamp should be described as a nonohmic device; a metal wire at a constant temperature is an ohmic device The use of non-ideal voltmeters is confined to voltmeters with a constant but finite resistance The use of non-ideal ammeters is confined to ammeters with a constant but non-zero resistance

Application of Kirchhoffs circuit laws will be limited to circuits with a maximum number of two sourcecarrying loops Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Data booklet reference: Kirchhoffs circuit laws: = 0 (loop)loop) = 0 (loop)junction); Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents International-mindedness:

A set of universal symbols is needed so that physicists in different cultures can readily communicate ideas in science and engineering Theory of knowledge: Sense perception in early electrical investigations was key to classifying the effect of various power sources, however this is fraught with possible irreversible consequences for the scientists involved. Can we still ethically and safely use sense perception in science research? Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Utilization: Although there are nearly limitless ways that we use electrical circuits, heating and lighting are two of the most widespread Sensitive devices can employ detectors capable of measuring small variations in potential difference

and/or current, requiring carefully planned circuits and high precision components Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Resistance If you have ever looked inside an electronic device you have no doubt seen what a __________ looks like. A resistors working part is usually made of ______, which is a _________________. The less carbon there is, the harder it is for current to flow through the resistor. As the animation shows, carbon is spiraled away to __________________ ____________________________________________

Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Resistance Some very precise resistors are made of wire and are called ________________________. And some resistors can be made to vary their resistance by tapping them at various places. These are called ___________________ and _______________. ____________ are temperaturedependent resistors, ___________ their ________________________ ___________________________. _______________________ (LDRs)LDRs) ________________________________ ________________________________. Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Resistance

__________________ R is a measure of __________ ________________________________l. Resistance is ___________________________________________. 0.L 0.0 330.4 This resistor has a resistance of _________. FYI A reading of 0.L on an ohmeter means overload. The resistance is too high to record with the meter. Topic 5: Electricity and magnetism

5.2 Heating effect of electric currents Resistance The different types of resistors have different ___________________________. _________________ 2 leads _____________ 3 leads ______________ 2 leads Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Resistance The different types of resistors have different schematic symbols. ______________ __________ ______________

2 leads 2 leads As ___________________ ______________________ As ___________________ _____________________ Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Resistance The resistance R of a material is the ratio of the potential difference V across the material to the current I flowing through the material. electric resistance The units from the formula are (loop)V A-1) which are called ohms (loop)). PRACTICE:

A fixed resistor has a current of 18.2 mA Orange = 3 when it has a 6.0 V potential difference Orange = 3 across it. What is its resistance? Brown = 1 SOLUTION: __________________________. Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Resistance To understand electrical resistance, consider two identical milk shakes. In the first experiment Resistance is a the straws have the measure of how same diameter, but hard it is to pass

different lengths. something through a material. In the second experiment the 1 straws have the same length, but different diameters. Note that _______ Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Resistance Of course conductors and resistors are not hollow like straws. And instead of milk shake

current we have electrical current. Even through solids _________. But __________________________ ______________________________. For example the exact same size of copper will have much less resistance than the carbon. With the ______________________ we have equality: resistance equation Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Resistance The Greek ______________________ of the particular material the resistor is made from. It is measured in m. Resistivities and Temperature Coefficients for Various Materials at 20C Material

(loop)m) (loop)C -1) Conductors Material (loop)m) (loop)C -1) 360010-8 -5.010-4 Semiconductors Aluminum

2.8210-8 4.2910-3 Carbon Copper 1.7010-8 6.8010-3 Germanium 4.610-1 -5.010-2

1010-8 6.5110-3 Silicon 2.5102 -7.010-2 Mercury 98.410-8 0.8910-3 Nichrome 10010-8

0.4010-3 Nickel 7.810-8 6.010-3 Platinum 1010-8 3.9310-3 1.5910-8 6.110-3

5.610-8 4.510-3 Iron Silver Tungsten Nonconductors Glass 1012 Rubber 1015 Wood

1010 Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Resistance Note that resistance depends on temperature. The IBO does not require us to explore this facet of resistivity. PRACTICE: What is the resistance of a 0.00200 meter long carbon core resistor having a core diameter of 0.000100 m? Assume the temperature is 20 C. From the table m. L

A Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Ohms law The German Ohm studied resistance of materials in the 1800s and in 1826 stated: Provided the temperature is kept constant, _________________________ _________________________________ _____________________________, and therefore the ______________________ _______________________________. In formula form Ohms law looks like this: Ohms law FYI Ohms law applies to components with constant R.

Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Ohms law ohmic and non-ohmic behavior A material is considered _________ if it behaves according to Ohms law. In other words _____________ ____________________________________________. EXAMPLE: Label appropriate V-I graphs with the following labels: ohmic, non-ohmic, R increasing, R decreasing, R constant. V V V SOLUTION: First label the resistance dependence. I I ___________________________________________ Ohms law states the R is constant. Thus __________ ______________________.

I Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Ohms law ohmic and non-ohmic behavior EXAMPLE: The graph shows the applied voltage V vs. resulting current I through a tungsten filament lamp. Find R when I = 0.5 mA and 1.5 mA. Is this filament ohmic or non-ohmic? SOLUTION: At 0.5 mA: V At 1.5 mA: V Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents

Ohms law ohmic and non-ohmic behavior EXAMPLE: The graph shows Material (loop)m) (loop)C ) the applied voltage V vs. Tungsten 5.610 4.510 resulting current I through a tungsten filament lamp. Explain why a lamp filament might be non-ohmic. SOLUTION: The temperature coefficient for tungsten is positive, typical for conductors. Therefore, __________________________________. But the _____________________________________. Thus, the ______________________________.

-1 -8 -3 Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Ohms law ohmic and non-ohmic behavior EXAMPLE: The I-V characteristic is shown for a non-ohmic component. the I-V characteristic for a ohmic component in the range V to 6.0 V. SOLUTION: Ohmic means and is the graph is linear).

Sketch in 40 of 0.0 constant (loop)and Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Power dissipation Recall that ________ is the rate at which work is being done. Thus . From Topic 5.1 we learned that . Thus FYI This power represents the energy per unit time delivered to, or consumed by, an electrical component having a current I and a potential difference V.

Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Power dissipation PRACTICE: Use the definition of resistance . together with the one we just derived (loop)) to derive the following two formulas: (loop)a) (loop)b) . SOLUTION: (loop)a) From (loop)b) From electrical power Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Power dissipation PRACTICE: The graph shows the V-I

characteristics of a tungsten filament lamp. What is its power consumption at I = 0.5 mA and at I = 1.5 mA? SOLUTION: solder joints Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Electric circuits An ____________ is a set of ___________ (loop)like wires) and __________ (loop)like resistors, lights, etc.) connected to an electrical ______________(loop)like a cell or a battery) in such a way that current can flow in complete loops. Here are two circuits consisting of ________________ _______________________. Note ___________________________ in each circuit. triple-loop circuit

single-loop circuit Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Circuit diagrams this is really A complete circuit will always a cell contain a cell or a battery. The _________________ of a cell is this: this is a battery A ________ is just a group this is the same of _____________________: battery If each cell is 1.5 V, then the battery above is _______. What is the voltage of your calculator battery?

A _______________ looks like this: this is a The schematic of a fixed-value resistor resistor looks like this: Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Drawing and interpreting circuit diagrams EXAMPLE: Draw schematic diagrams of each of the following circuits: SOLUTION: Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Investigating combinations of resistors in series R2 R3

R1 Resistors can be connected to one another in series, which means one after the other. Note that there is only one current I and that ________ ____________________________________________. Conservation of energy tells us q = Thus = IR1 + IR2 + IR3 = I(loop)R1 + R2 + R3) = I(loop)R), where __________________ equivalent resistance in series Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Investigating combinations of resistors in series R2 R3

R1 EXAMPLE: Three resistors of 330 each are connected to a 6.0 V battery in series as shown. (loop)a) What is the circuits equivalent resistance? (loop)b) What is the current in the circuit? SOLUTION: (loop)a) In series, R = R1 + R2 + R3 so that R= (loop)b) Since the voltage on the entire circuit is 6.0 V, and since the total resistance is 990 , from Ohms law we have Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Investigating combinations of resistors in series R2

R3 R1 EXAMPLE: Three resistors of 330 each are connected to a 6.0 V battery in series as shown. (loop)c) What is the voltage on each resistor? SOLUTION: (loop)c) The current I we just found is the same everywhere. Thus each resistor has a current of I = From Ohms law, each resistor has a voltage given by = FYI ___________________________________________. Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Investigating combinations of resistors in parallel

Resistors can also be in parallel. In this circuit each resistor is R2 R3 R1 connected directly to the cell. Thus each resistor has the same voltage V and _________________________________ We can then write = _______________________. But there are three currents I1, I2, and I3. Since the total current I passes through the cell we see that I = _______________ If R is the equivalent or total resistance of the three resistors, then I = I1 + I2 + I3 becomes ___________________ Continued Topic 5: Electricity and magnetism

5.2 Heating effect of electric currents Investigating combinations of resistors in parallel Resistors can also be in parallel. In this circuit each resistor is R2 R3 R1 connected directly to the cell. Thus each resistor has the same voltage V and V is the same for all parallel components. Continued From = V1 = V2 = V3 V and , we get Thus the equivalent resistance R is given by equivalent resistance in parallel Topic 5: Electricity and magnetism

5.2 Heating effect of electric currents Investigating combinations of resistors in parallel EXAMPLE: Three resistors of 330 each are connected to a R2 R3 R1 6.0 V cell in parallel as shown. (loop)a) What is the circuits resistance? (loop)b) What is the voltage on each resistor? SOLUTION: (loop)a) In parallel, so that (loop)b) The voltage on each resistor is Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Investigating combinations of resistors in parallel EXAMPLE: Three resistors of

330 each are connected to a R2 R3 R1 6.0 V cell in parallel as shown. (loop)c) What is the current in each resistor? SOLUTION: (loop)c) Using Ohms law : FYI ______________ _______________ _______________ Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Circuit diagrams - voltmeters are connected in parallel PRACTICE: Draw a schematic diagram

for this circuit: 1.06 SOLUTION: FYI Be sure to position the _________ across the desired resistor ______________. lac e ten ths p Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents

Circuit diagrams - voltmeters are connected in parallel EXAMPLE: 09.4 00.0 A batterys voltage is measured as shown. (loop)a) What is the uncertainty in its measurement? SOLUTION: For _____________ always use __________________________ ________________________________. For this voltmeter the voltage is measured to the tenths place so we give the raw uncertainty a value of V = ________. Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Circuit diagrams - voltmeters are connected in parallel

EXAMPLE: 09.4 A batterys voltage is measured as shown. (loop)b) What is the fractional error in this measurement? SOLUTION: Fractional error is just . For this particular measurement we then have FYI When using a voltmeter the __________________________ __________________________________________ Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Circuit diagrams - voltmeters are connected in parallel Consider the simple circuit of battery, lamp, and wire. To measure the

_________ of the circuit we merely 01.6 00.0 connect the voltmeter while the circuit is in operation. lamp cell voltmeter in parallel Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Circuit diagrams - ammeters are connected in series To measure the ________ of the circuit we must break the circuit and insert the _________ so that it intercepts

all of the electrons that normally 00.2 00.0 travel through the circuit. ammeter _________ lamp cell Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents the circuit must be temporarily broken to insert

the ammeter Circuit diagrams - ammeters are connected in series PRACTICE: Draw a schematic diagram for this circuit: .003 SOLUTION: FYI Be sure to position the ______________ between the desired resistors __________. Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Circuit diagrams PRACTICE: Draw a schematic diagram for this circuit: SOLUTION:

FYI This circuit is a combination series-parallel. In a later slide you will learn how to find the equivalent resistance of the combo circuit. Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Ideal voltmeters - resistance _____________________________. The voltmeter _________________ _____________________________ __________________________. The green current represents the amount of current the battery needs to supply to the voltmeter in order to make it register. The red current is the amount of current the battery supplies to the original circuit. In order to NOT ALTER the original properties of the circuit, ______________________________________

__________________ to minimize the green current. Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Ideal ammeters - 0 resistance ________________________ __________________. The ammeter is supposed to read the current of the original circuit. In order to NOT ALTER the original properties of the circuit, ______________________________________ ___________ to minimize the effect on the red current. Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Potential divider circuits potential Consider a battery of = 6 V. R1 divider

Suppose we have a light bulb that can only use three volts. How do we obtain 3 V from a R2 6 V battery? A ________________ is a ____________________________________________ ____________________________________________ _________________________ The ________________ is the emf of the battery. The ________________ is the voltage drop across R2. Since the _______________________________. Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Potential divider circuits Consider a battery of = 6 V. Suppose we have a light bulb that can only use three volts.

How do we obtain 3 V from a 6 V battery? From Ohms law the current of the divider is given by But so that R1 potential divider R2 potential divider Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Potential divider circuits

PRACTICE: Find the output voltage if the battery has an emf of 9.0 V, R1 is a 2200 resistor, and R2 is a 330 resistor. SOLUTION: FYI The bigger R2 is in comparison to R1, the closer VOUT is in proportion to the total voltage. Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Potential divider circuits PRACTICE: Find the value of R2 if the battery has an emf of 9.0 V, R1 is a 2200 resistor, and we want an output voltage of 6 V.

SOLUTION: Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Potential divider circuits PRACTICE: A light-dependent resistor (loop)LDR) has R = 25 in bright light and R = 22000 in low light. An electronic switch will turn on a light when its p.d. is above 7.0 V. What should the value of R1 be? SOLUTION: Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Potential divider circuits PRACTICE: A thermistor has a resistance of 250 when it is in the heat of a fire and a resistance

of 65000 when at room temperature. An electronic switch will turn on a sprinkler system when its p.d. is above 7.0 V. (loop)a) Should the thermistor be R1 or R2? SOLUTION: Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Potential divider circuits PRACTICE: A thermistor has a resistance of 250 when it is in the heat of a fire and a resistance of 65000 when at room temperature. An electronic switch will turn on a sprinkler system when its p.d. is above 7.0 V. (loop)b) What should R2 be? SOLUTION: In fire the thermistor is .

Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Potential divider circuits PRACTICE: A filament lamp is rated at 4.0 V, 0.80 W on its package. The potentiometer has a resistance from X to Z of 24 and has linear variation. (loop)a) Sketch the variation of the p.d. V vs. the current I for a typical filament lamp. Is it ohmic? SOLUTION: Since the temperature increases with the current, so does the resistance. Topic 5: Electricity and magnetism

5.2 Heating effect of electric currents Potential divider circuits R1 PRACTICE: A filament lamp is rated R2 at 4.0 V, 0.80 W on its package. The potentiometer has a resistance from X to Z of 24 and has linear variation. (loop)b) The potentiometer is adjusted so that the meter shows 4.0 V. Will its contact be above Y, below Y, or exactly on Y? SOLUTION: Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Potential divider circuits R1 PRACTICE: A filament lamp is rated

R2 at 4.0 V, 0.80 W on its package. The potentiometer has a resistance from X to Z of 24 and has linear variation. (loop)c) The potentiometer is adjusted so that the meter shows 4.0 V. What are the current and the resistance of the lamp at this instant? SOLUTION: W and V. Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Potential divider circuits R1 PRACTICE: ContinuedThe potentiometer R2 has a resistance from X to Z of 24

and has linear variation. (loop)d) The potentiometer is adjusted so that the meter shows 4.0 V. What is the resistance of the Y-Z portion of the potentiometer? SOLUTION: Let = X to Y and = Y to Z resistance. Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Potential divider circuits R1 PRACTICE: A filament lamp is rated R2 at 4.0 V, 0.80 W on its package. The potentiometer has a resistance from X to Z of 24 and has linear variation. (loop)e) The potentiometer is adjusted so that the meter shows 4.0 V. What is the current in the Y-Z

portion of the potentiometer? SOLUTION: Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Potential divider circuits R1 PRACTICE: A filament lamp is rated R2 at 4.0 V, 0.80 W on its package. The potentiometer has a resistance from X to Z of 24 and has linear variation. (loop)f) The potentiometer is adjusted so that the meter shows 4.0 V. What is the current in the ammeter? SOLUTION: Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents

Solving problems involving circuits PRACTICE: A battery is connected to a 25-W lamp as shown.What is the lamps resistance? SOLUTION: 01.4 00.0 Suppose we connect a voltmeter to the circuit. We know W. We know V. Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Solving problems involving circuits PRACTICE: Which circuit shows the correct setup to find the V-I characteristics of a filament lamp? SOLUTION:

Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Solving problems involving circuits PRACTICE: A non-ideal voltmeter is used to measure the p.d. of the 20 k resistor as shown. What will its reading be? SOLUTION: There are two currents in the circuit because the voltmeter does not have a high enough resistance to prevent the green one from flowing. The 20 k resistor is in parallel with the 20 k Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Solving problems involving circuits PRACTICE: All three circuits use the same resistors and the same cells. Which one of the following

shows the correct ranking for the currents passing through the cells? SOLUTION: Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Solving problems involving circuits PRACTICE: The voltmeter has infinite resistance. What are the readings on the voltmeter when the switch is open and closed? SOLUTION: E Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents

Kirchhoffs rules junction, branch, and loop _________a circuit consists of ___________ ____________________________________. Consider the following circuit containing a few batteries and resistors: Kirchhoff A ________ is a point in a circuit where three or more _____________________________. A ________ is all the ________ __________________________ ________________________. A _______ is all the _______ ________________________ Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Kirchhoffs rules the rule for current I Solving a circuit consists of finding the voltages and currents of all of its components.

STEP 1: Assign a current to each branch. If you have a good idea which way it flows, choose that direction. If you dont, an arbitrary direction will do just fine. I1 I3 FYI If a current turns out to have a negative solution, you will interpret that as meaning that it I2 flows in the opposite direction. Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Kirchhoffs rules the rule for current I Solving a circuit consists of finding the voltages and currents of all of its components.

If a current enters a junction it is a gain and is assigned a POSITIVE value. If a current leaves a junction it is a loss and is assigned a NEGATIVE value. For the TOP junction, I1 and I3 I1 I3 are both POSITIVE and I2 is NEGATIVE. For the BOTTOM junction, I1 and I3 are both NEGATIVE I2 and I2 is POSITIVE. Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Kirchhoffs rules the rule for current I Solving a circuit consists of finding the voltages and currents of all of its components.

From conservation of charge the sum of the currents at each junction is zero. I = 0 (loop)junction) STEP 2: Use Kirchhoffs rule for I for each junction. Each JUNCTION yields its own equation: TOP: I1 I2 + I3 = 0. BOTTOM: I2 I1 I3 = 0. Kirchhoffs rule for I I1 I3 I2 Topic 5: Electricity and magnetism

5.2 Heating effect of electric currents Kirchhoffs rules the rule for voltage V Solving a circuit consists of finding the voltages and currents of all of its components. ____________________________ and each ____________________________. ____________________________________________ __________________________________. Since the _________________, ________________________ ________________________ _______________________. We can go either CW or CCW it doesnt matter. Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Kirchhoffs rules the rule for voltage V Solving a circuit consists of finding the

voltages and currents of all of its components. If our _______________________________ ____________________________________ ______________________________. If our loop goes ______ the branch current, the _____ __________________________. I3 I1 V2 V4 1 V3 2 For our loop we see that we V1 I2 have _______________________. Topic 5: Electricity and magnetism

5.2 Heating effect of electric currents Kirchhoffs rules the rule for voltage V Solving a circuit consists of finding the voltages and currents of all of its components. If __________________________________ ____________________________________ ________________________. If our loop goes from _______________ through a cell the ______________________. I1 I3 V2 V4 1 V3 2 For our loop we see that we V1 I2

have_____________________ Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Kirchhoffs rules the rule for voltage V Solving a circuit consists of finding the voltages and currents of all of its components. From __________________________ the _____________________________ ____________________. Kirchhoffs rule for V STEP 3: Use Kirchhoffs rule for V for each loop. For our loop we have FYI The qs all cancel. V2 1

V1 I1 I3 V4 2 V3 I2 Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Kirchhoffs rules the rule for voltage V Solving a circuit consists of finding the voltages and currents of all of its components. From conservation of energy the sum of the voltages in each

loop is zero. (loop)loop) PRACTICE: Using the voltage rule write the equation for the other loop. SOLUTION: Kirchhoffs rule for V V2 1 V1 I1 I3 V4 2

V3 I2 Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Kirchhoffs rules solving the circuit EXAMPLE: Suppose each of the resistors is R = 2.0 , and the emfs are 1 = 12 V and 2 = 6.0 V. Find the voltages and the currents of the circuit. SOLUTION: Use Ohms law: for the resistors. From the rule for we have __________________ From the rule for we have From Ohms law we have Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Kirchhoffs rules solving the circuit EXAMPLE: Suppose each of the resistors is R = 2.0 ,

and the emfs are 1 = 12 V and 2 = 6.0 V. Find the voltages and the currents of the circuit. SOLUTION: We now have three equations in I. V2 1 V1 I1 I3 V4 2 V3 I2

Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Kirchhoffs rules solving the circuit EXAMPLE: Suppose each of the resistors is R = 2.0 , and the emfs are 1 = 12 V and 2 = 6.0 V. Find the voltages and the currents of the circuit. SOLUTION: Now eliminate variables one by one. (loop)1) . (loop)2) . (loop)3) . (loop)1) into (loop)3) eliminates : I1 I3 V2 V4 Then 1 Placing into (loop)2) yields

V3 2 V1 I2 Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Kirchhoffs rules solving the circuit EXAMPLE: Suppose each of the resistors is R = 2.0 , and the emfs are 1 = 12 V and 2 = 6.0 V. Find the voltages and the currents of the circuit. SOLUTION: Once you have one, you have them all by substitution: (loop)1) . (loop)2) . (loop)3) . Putting into (loop)2): I1 I3

V2 V4 Putting and into (loop)1): 1 V3 2 Since and are negative, V1 I2 we ______________________. Topic 5: Electricity and magnetism 5.2 Heating effect of electric currents Kirchhoffs rules solving the circuit EXAMPLE: Suppose each of the resistors is R = 2.0 , and the emfs are 1 = 12 V and 2 = 6.0 V. Find the voltages and the currents of the circuit. SOLUTION:

Finally, we can redraw our currents: From Ohms law we calculate our resistor voltages: V2 Use both of Kirchhoffs rules to check junctions and loops. V4 V3 V1