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 = 0.6 A  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

Three light bulbs with resistance R 1 = 1 , R 2 = 2  and R 3 = 3  are connected in series to a battery. Which has the largest potential drop across it? A)R 1 B)R 2 C)R 3 D)All have the same potential drop E)It depends on the voltage of the battery

A string of Christmas trees lights are connected in series. If one light is removed and replaced with a normal wire, A)The other lights get dimmer B)The other lights get brighter C)The other lights don’t change D)It depends on the current in the wire E)It depends on the voltage across the wire

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: C =  0 A/d   How can we combine capacitors in circuits?

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

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

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 +- VV C1C1 C2C

Capacitors in Circuits   Can resolve every series or parallel group into one capacitor 

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 (  )  = RC  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 V C =  [1-e (-t/  ) ]   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