Physics 232C Topic 17e Kirchhoff s Laws Physics 232C Kirchhoff s Junction or Current Law Kirchhoff s Junction or Current Law Conservation of Charge conservation of current The net charge flowing into a point must exactly equal the net charge flowing out of the point We already saw this I1 I2 I3 1I 2I At a junction in a circuit 3I I in I out Physics 232C 1 2 1 Kirchhoff s Voltage or Loop Law Kirchhoff s Voltage or Loop Law If a charge travels around a loop and returns to its starting location The net change in potential energy is zero Summing the voltage changes around the circuit must be zero This is really a statement of conservation of energy Voltage changes can be positive or negative Circuit elements below can be any type of element 1V 2V 3V Loop law V1 V2 V3 0 0V Physics 232C Using Kirchhoff s Laws Using Kirchhoff s Laws If you are not given a circuit diagram draw one Label all currents if you don t know a direction guess If your guess is incorrect the resulting current will be negative Generating Equations use the junction law and loop law to generate enough equations to solve for all unknowns Apply the junction current law at nodes to get current I equations in I 2 I 1 I 4 I out Physics 232C 3 4 2 Using Kirchhoff s Laws Using Kirchhoff s Laws Generating Equations continued Apply the loop law by starting at any point in your circuit and adding up all of the voltage changes around a closed loop until you return back to your starting point 0V Batteries V 0 moving from negative terminal to positive V 0 moving from positive terminal to negative Resistors V 0 moving opposite current direction V 0 moving in same direction as current I R I R 1 1 4 0 4 In general you can generate more than one loop equation and more than one junction equation Physics 232C Concept Check 1 Concept Check 1 What is the current IA Pay attention to the arrows and whether they are pointing towards or away from a junction 5 A 4 A IA IB 2 A Physics 232C 5 6 3 Concept Check 2 Concept Check 2 If the voltage across R1 following the direction indicated by loop 1 is 4 volts and 1 9 volts what is the voltage supplied by the second battery Use Kirchhoff s Loop Law Physics 232C Physics 232C Physics 232C Topic 17f Series and Parallel Circuits 7 8 4 Parallel and Series Circuits review Parallel and Series Circuits review Consider the possible paths within each circuit to get from point A to point B through wires and or circuit elements Parallel more than one path through the circuit elements Series only one path possible through circuit elements A B A B To simplify such circuits we need to find a single equivalent capacitance for both the parallel case and the series case In general a circuit is a combination of elements connected in parallel and series Physics 232C 9 Equivalent Series Resistance Equivalent Series Resistance The current is the same everywhere in a series circuit V1 V2 0 VR 0 SR R R 1 2 The equivalent series is larger than the resistance of any of the resistors connected in series Physics 232C 10 5 Series Resistors Series Resistors Let s use Kirchhoff to check RS R1 R2 Same current V1 V2 0 IR1 IR2 0 I R1 R2 0 I R1 R2 I 1 R R 2 VR 0 IRS 0 I R1 R2 0 I R1 R2 I 1 RR 2 Physics 232C 11 Power for Series resistors Power for Series resistors Power in series resistors V1 I1 R1 V2 I2 R2 Remember that in general PR I V So in this case since I1 I2 P1 I V1 P2 I V2 V 1 V 2 P 1 P 2 R 1 R 2 More power is dissipated in the resistor having the larger resistance Physics 232C 12 6 Parallel resistors Parallel resistors Key Facts Battery applies the same voltage across each resistor The current is not the same across each resistor in general V 1 V 2 I 2 bI I 1 V V 2 1 I R I R 1 1 2 2 2 I I 1 R 1 R 2 Physics 232C 13 Equivalent Parallel Resistance Equivalent Parallel Resistance To find RP we ll use 1 2 V 1 bI V 2 I I 1 2 Starting from 2 Ib I1 I2 R PR 2 1 1 PR R 2 R 1 1 R 1 Resistance gets smaller as you add more R in parallel The equivalent parallel resistance is smaller than the resistance of any of the resistors connected in parallel 1 PR 1 R 1 1 R 2 1 R 1 1 R 2 1 PR Physics 232C 14 7 Power for Parallel Resistors Power for Parallel Resistors Remember that in general PR I V And in this case V1 V2 R and 1 R 2 I I 2 1 P1R1 P2R2 So P1 I1 V1 I1 P2 I2 V2 I2 P 1 P 2 I I 1 2 R 2 R 1 Smaller resistor dissipates more power Physics 232C 15 Measuring Voltage and Current Measuring Voltage and Current Current is measured with an ammeter which should be inserted in series with the circuit element in question so they have the same current flowing through each of them The internal resistance of the ammeter should be very small compared to the resistors in the circuit Otherwise the meter itself will add to the series resistance and reduce the current it is trying to measure Physics 232C 16 8 Measuring Voltage and Current Measuring Voltage and Current Voltage is measured with an voltmeter which should be inserted in parallel across the circuit element in question The internal resistance of the voltmeter should be very large compared to the resistors in the circuit Otherwise the meter itself will draw current and reduce the voltage it is trying to measure Physics 232C 17 Household Electricity Household Electricity Neutral or grounded side Grounds the metal case on appliances Physics 232C 18 9 Household Electricity 2 Household Electricity 2 on off switch circuit breaker Reference point where V 0 V Are your devices appliance connected in parallel or series with each other Parallel Supplies 120 V for each appliance but increases the current if current becomes too high will trip the circuit breaker Physics 232C 19 Physics 232C Example 17d Equivalent Resistance Physics 232C 20 10 Parallel Circuit 1 Parallel Circuit 1 You are handed 3 identical 1 resistors which are connected in parallel If you want to replace the 3 resistors with 1 resistor what equivalent resistance do you need Physics 232C 21 Series and Parallel Series and Parallel What is the equivalent resistance for the circuit below if R1 1 R2 1 and R3 3 A B C 1 D 2 E 3 R3 Physics 232C 22 11 Concept Check 1 Concept Check 1 How does the brightness of bulb B compare to bulb …