1. RC Circuits Physics 102 Professor Lee Carkner Lecture 16

2. Series and Parallel    V = 6 for each branch so I 2 =  V/R = 6/6 = 1 A and I 3 =  V/R = 6/10 = 0.6 A   Equivalent resistance total: 1/R eq = 1/6 +1/10, R eq = 3.75  so I 1 = I eq =  V/R eq = 6/3.75 = 1.6 A through battery (  V=6) + -  V = 6 V 10   4  6  I1I1 I3I3 I2I2

3. Kirchhoff’s Rules  Left loop: 6 - 6I 2 = 0   Right loop: 6I 2 - 6I 3 - 4I 3 = 0   I 1 = I 2 +I 3   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

4. Kirchhoff Tips  Find the currents   Each single branch has a current   Indicate current direction   Apply junction rule  Currents in equal currents out

5. More Kirchhoff Tips  Apply the loop rule  Sum of all  V equal to zero   From - to + terminal the  V is equal to +    Moving with the current the  V is - IR   Solve equations  Need as many equations as unknowns   Check your work

6. Today’s PAL  Use Kichhoff’s rules to find the current through each resistor

7. Capacitance   The value of C depends on its physical properties: C =  0 A/d   How can we combine capacitors in circuits?

8. 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

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

10. Capacitors in Series  Charge stored by each is the same (Q)  Equivalent capacitor also has a charge of Q   Since  V = Q/C:   The equivalent capacitance is:  1/C eq = 1/C 1 + 1/C 2 +- VV C1C1 C2C2 + -- +

11. 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

12. 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

13. Charging a Capacitor

14. Charge on the Capacitor   We can write an expression for the charge on a capacitor: Q(t) = C  [1-e (-t/  ) ]  Capacitor charges rapidly at first and then the rate of charge separation slows   At about t = 4  the capacitor is nearly fully charged

15. Time Curve

16. Meters  We use meters to measure current, resistance, capacitance, voltage, etc.    Want to minimize their effect

17. Using an Ammeter

18. Using a Voltmeter

19. Types of Meters  Ammeter   Must be placed in series   Voltmeter   Must be placed in parallel 

20. Next Time  Read 22.1-22.2  Homework Ch 21, P: 29, Ch 22, P: 2  Final:  Section 1: Tuesday, Feb 25, 9-11 am  Section 2: Thursday, Feb 27, Noon-2pm