1. AP Physics C
DC Circuits

2. Resistors in Series What is constant? What ‘adds up’? How do you
determine the
equivalent resistance?

3. Sample Problem #1
The current flowing in a circuit containing four resistors connected in series is I = 1.0 A. The potential drops across the first, second and third resistors are, respectively: V = 5 V, V = 8 V and V = 7 V. The equivalent resistance of the circuit is R = 30. Find the total voltage supplied by the battery, and also current, voltage drop, and resistance of each resistor in the circuit. V I R P 1 5
1.0 2 8 3 7 4 EQ 30

4. Resistors in Parallel What is constant? What ‘adds up’? How do you
determine the
equivalent resistance?

5. Sample Problem #2 Complete the VIRP Table for the circuit shown. V I R1
2.0 2
3.0 3
6.0 Eq
12.0

6. Sample Problem #3 Resistors in Combination or a Network of Resistors V1
10.0 2
4.0 3
3.0 4
8.0 5
1.0 Eq
13.4

7. Sample Problem #4
Determine the equivalent resistance:

8. Kirchhoff’s Rules
Current (Point) Rule: The total current into a junction is equal to the current out of a junction or the total current is zero.

9. Kirchhoff’s Rules
Voltage (Loop) Rule: The total voltage gains of the sources is equal to the total voltage drops of the loads or the total gains and drops is
zero.

10. Problem-Solving Strategy:
Determine and label the direction of the current in the given circuit.
Apply the point rule once and then the loop rule as many times as needed to get the same number of equations as unknowns in the circuit. Note: Follow the sign convention given on the next slide when apply the loop rule.

11. Sign Convention for the Loop Rule:
The loop is going from left to right.

12. Sample Problem #5
Find the currents:

13. Sample Problem #6
Find the currents:

14. Ammeter Design

15. Voltmeter Design

16. Sample Problem #7
The resistance of a galvanometer coil is 20 Ω and the full-scale current is 50 μA.
What does the resistance of the shunt need to be to design an ammeter that would measure up to 5.0 A?
What does the resistance of the series resistor need to be to design a voltmeter that would measure up to 100 V?

17. RC Circuits Initially, the capacitor is uncharged.
What is the current in the circuit when the switch is closed; that is, at t = 0?
How does the current change over time?
What is the charge stored on the capacitor at t = 0?
How does the charge change
over time?

18. Charging a RC Circuit Apply Kirchhoff’s Loop Rule:
Recall the definition for
current

19. Time Constant-Characteristic Property of a RC Circuit

20. Transient Values when charging a RC Circuit
At t = 0
Some t later
As t  ∞
Capacitor
Current
Voltage
Resistor

21. Discharging a RC Circuit
The capacitor has been fully charged. The source of emf has been removed. What is the current in the circuit when the switch is closed; that is, at t = 0?
What happens to the current over time?
What is the charged stored on the capacitor at t = 0?
What happens to the charge over time?

22. Discharging a RC Circuit:
When the capacitor is fully charged, the switch is moved from a to b.
Apply Kirchhoff’s loop rule,

23. Voltage-Time Graphs
Sketch the Voltage-Time Graphs for discharging a RC Circuit

24. Transient Values when discharging a RC Circuit
At t = 0
Some t later
As t  ∞
Capacitor
Current
Voltage
Resistor

25. The circuit above has been in position a for a long time
The circuit above has been in position a for a long time. At time t = 0 the switch is thrown to position b. DATA: Vb = 12 V, C = 10 μF, R = 20 Ω
What is the curnent through the resistor just BEFORE the switch is thrown?
What is the current through the resistor just AFTER the switch is thrown?
What is the charge across the capacitor just BEFORE the switch is thrown?
What is the charge on the capacitor just AFTER the switch is thrown?
What is the charge on the capacitor at at time t = 0.3 msec after the switch is thrown?

26. Considering the same circuit, only with the switch thrown from b to a at time t = 0 after having been in position b for a long time. DATA: Vb = 12 V, C = 10 μF, R = 20Ω
What is the curnent through the resistor just BEFORE the switch is thrown?
What is the current through the resistor just AFTER the switch is thrown?
What is the charge across the capacitor just BEFORE the switch is thrown?
What is the charge on the capacitor just AFTER the switch is thrown?
What is the charge on the capacitor at at time t = 0.3 msec after the switch is thrown?