1. RC Circuits Physics 102 Professor Lee Carkner Lecture 15

2. Kirchhoff’s Rules  Left loop: 6 - 6I 2 = 0  6 = 6I 2 so I 2 = 1 A  Right loop: 6I 2 - 6I 3 - 4I 3 = 0  Since I 2 = 1, 6 -10I 3 = 0, or 6 = 10I 3 or I 3 = 0.6 A  I 1 = I 2 +I 3  I 1 = 1 + 0.6 or I 1 = 1.6 A  Voltage: For battery  V = 6 V, for 6 ,  V = 6I 2 = 6 V, for 2nd 6 ,  V = 6I 3 = 3.6 V, for 4 ,  V = 4I 3 = 2.4V + -  V = 6 V  4  6  I1I1 I3I3 I2I2

3. Kirchhoff Tips  Current  Currents are bounded by junctions   Each single branch has a current   Voltage   Only include batteries (  ) 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  V  How can we combine capacitors in circuits?

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

6. Capacitors in Parallel  Potential difference across each is the same (  V)   But:  Q 1 = C 1  V  Q 2 = C 2  V   The equivalent capacitance is:  C eq = C 1 + C 2 +- VV C1C1 C2C2

7. Capacitors in Series  Charge stored by each is the same (Q)   Total  V is the sum (  V =  V 1 +  V 2 )  Since  V = Q/C:   The equivalent capacitance is:  1/C eq = 1/C 1 + 1/C 2  Only the outer plates have a net charge build-up +- VV C1C1 C2C2 + -- +

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   = 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  Q C = CV C V C =  [1-e (-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? A)Increases : Increases B)Decreases : Decreases C)Increases : Decreases D)Decrease : Stay the same E)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? A)Increases : Increases B)Decreases : Decreases C)Increases : Decreases D)Decrease : Same E)Same : Same