1. AP Physics L09_circuits containing resistors
Electric Circuits
containing resistors

2. Circuits
Charges travel in a circuit to maintain charge balance

3. Resistance Current does not flow unhindered
Electrical resistance is analogous to friction or drag
Expressed as potential needed to maintain a current

4. Circuit Diagrams
Potential source
resistor

5. Kirchoff’s Laws Current into any node equals current out of the node
I1 = I2 + I3 0 = I2 + I3 – I1
“Current law”
“Junction law”
Conservation of charge

6. Kirchoff’s Laws Potential drop around any closed loop is zeroV1
V – V1 – V2 = 0
V1 + V2 = V V
“Voltage law”
“Loop law” V2
Conservation of energy

7. Question: Series Circuit
Circuit resistance is
A. More than with one bulb. B. Less than with one bulb. C. The same as with one bulb.

8. Series Circuit R1 R2 R3
Circuit resistance = R1 + R2 + R3

9. Series Summary The same current flows through all resistors in series.
The series resistance is the sum of the resistors’ resistances.
The resistors’ voltage drops add up to the series total.
The voltage drop across a resistor is proportional to its resistance.

10. Question: Parallel Circuit
Circuit resistance is
A. More than with one bulb. B. Less than with one bulb. C. The same as with one bulb.

11. Parallel Circuit Diagram

12. Potential Differences

13. Currents Total current = I = I1 + I2 + I3 = V/R1 + V/R2 + V/R3
Circuit resistance =V/I =
1/R1 + 1/R2 + 1/R3 1

14. Parallel Summary
The same voltage drops across all resistors in parallel.
The series current is the sum of the resistors’ currents.
The effective resistance is less than for any individual resistor.
Formula is
R =

15. Series and Parallel Circuit
1/R2 + 1/R3 1
Circuit resistance = R1 +

16. Group Work
Determine current direction, current, voltage, and power dissipated for each resistor.
12 W
6 W
9 W
8 W
10 W
3 W
18 W
9 W
9 W
18 W

17. Group Work Determine the power for each resistor. 12 W 6 W 9 W 8 W

18. Using Kirchoff’s Rules
Make as many loop equations as there are unique loops.
Make as many node equations as there are branches.
The number of equations may depend on how much cleaning up you do beforehand.

19. Kirchoff’s Rules