1. RC Circuits Physics 102 Professor Lee Carkner Lecture 15

2. Kirchhoff’s Rules I1 I3 6 W I2 + • Left loop: 6 - 6I2 = 0 • 6 = 6I2 so I2 = 1 A • Right loop: 6I2 - 6I3 - 4I3 = 0 • Since I2 = 1, 6 -10I3 = 0, or 6 = 10I3 or I3 = 0.6 A • I1 = I2 +I3 • I1 = 1 + 0.6 or I1 = 1.6 A • Voltage: For battery DV = 6 V, for 6W, DV = 6I2 = 6 V, for 2nd 6W, DV = 6I3 = 3.6 V, for 4W, DV = 4I3 = 2.4V - DV = 6 V 6 W 4 W

3. Kirchhoff Tips • Current • Currents are bounded by junctions • Each single branch has a current • Voltage • Only include batteries (e) and resistors (IR)

4. Capacitance • Remember that a capacitor stores charge: • The value of C depends on its physical properties: • Note that capacitance does not depend on DV • How can we combine capacitors in circuits?

5. Simple Circuit C • Battery (DV) connected to capacitor (C) • The capacitor experiences potential difference of DV and has stored charge of Q = C DV - + Q + - DV

6. Capacitors in Parallel • Potential difference across each is the same (DV) • But: • Q1 = C1DV • Q2 = C2DV • The equivalent capacitance is: • Ceq = C1 + C2 C1 C2 + - DV

7. Capacitors in Series C1 C2 • Charge stored by each is the same (Q) • Total DV is the sum (DV = DV1 + DV2) • Since DV = Q/C: • The equivalent capacitance is: • 1/Ceq = 1/C1 + 1/C2 • Only the outer plates have a net charge build-up - - + + + - DV

8. Capacitors in Circuits • Remember series and parallel rules extend to any number of capacitors • Keep simplifying until you find the equivalent capacitance for the whole circuit

9. Resistors and Capacitors • If you add a resistor to a charged capacitor, the capacitor will discharge through it • If we charge a capacitor with a resistor in the circuit, it will also take time for the capacitor to fully charge t = RC • This is the time to charge a capacitor to about 63% of the final value

10. Charging a Capacitor

11. Time Curve

12. Charge Over Time QC = CVC VC= e[1-e(-t/t)] • Capacitor charges rapidly at first and then the rate of charge separation slows • As you charge the capacitor you increase the repulsive force which makes adding more charge harder

13. Next Time • Read: 20.1, 20.4 • Homework: Ch 19 P 31, 50, Ch 20 P 10, 11 • Quiz 2 next Monday (January 26)

14. Consider two resistors connected in series to a battery. One more resistor is then added in series. What happens to the current through each resistor : What happens to the (absolute value) of the voltage across each resistor? • Increases : Increases • Decreases : Decreases • Increases : Decreases • Decrease : Stay the same • Same : Same

15. Consider two resistors connected in parallel to a battery. One more resistor is then added in parallel. What happens to the current through each resistor : What happens to the (absolute value) of the voltage across each resistor? • Increases : Increases • Decreases : Decreases • Increases : Decreases • Decrease : Same • Same : Same