RC Circuits Physics 102 Professor Lee Carkner Lecture 16

Kirchhoff’s Rules  Left loop: 6 - 6I 2 = 0   Right loop: 6I 2 - 6I 3 - 4I 3 = 0  Since I 2 = 1, 6 -10I 3 = 0, or 6 = 10I 3 or I 3 =  I 1 = I 2 +I 3  I 1 = or I 1 =  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

Kirchhoff Tips  Current   Each single branch has a current   Voltage   Only include batteries and resistors

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?

Simple Circuit   Battery removes electrons from the left side and transfers them to the right  VV C Q

Capacitors in Parallel   Total stored charge is the sum (Q = Q 1 + Q 2 )  But:  Q 1 =  Q 2 =  Q =  The equivalent capacitance is:  C eq = C 1 + C 2 +- VV C1C1 C2C2

Capacitors in Series   Equivalent capacitor also has a charge of Q  Total  V is the sum (  V =  V 1 +  V 2 )   Q/C eq = Q/C 1 + Q/C 2   1/C eq = 1/C 1 + 1/C 2 +- VV C1C1 C2C

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

Resistors and Capacitors   After a certain amount of time, all the energy in the capacitor will go into heating the resistor   A capacitor C paired with a resistor R will have a time constant (  )   This is the time to charge a capacitor to about 63% of the final value

Charging a Capacitor

Time Curve

Charge Over Time  If we charge a capacitor by connecting it to a battery of voltage , the charge and voltage on the capacitor is: Q C = CV C   As you charge the capacitor you increase the repulsive force which makes adding more charge harder 

Next Time  Read: 20.1, 20.4  Homework: Ch 19 P 31, 50, Ch 20 P 10, 11  Quiz 2 next Friday