Capacitance (II) Capacitors in circuits Electrostatic potential energy

Capacitors in Circuits Symbols: or Capacitor  Battery  Switch 

Capacitor Combinations AB Series AB Parallel What is the “effective capacitance” between A & B? A B +Q -Q

Parallel C1C1 C2C2 C3C3 A B V Q1Q1 -Q 1 Q2Q2 -Q 2 Q3Q3 -Q 3 Voltages are the same: V 1 = V 2 = V 3 = … = V Charges add: But…

Series Voltages add: Charges are equal: And … +Q -Q +Q -Q +Q -Q C1C1 C3C3 C2C2 A B

Example 8uF 4uF 2uF 6uF 1uF 3uF b a Find the equivalent capacitance between a and b.

Solution

Example Find the equivalent capacitance between points a and b in the combination of capacitors shown below

Consider the circuit shown below, where C 1 = 6.00 μF, C 2 = 3.00 μF, and ΔV = 20.0 V. Capacitor C 1 is first charged by the closing of switch S 1. Switch S 1 is then opened, and the charged capacitor is connected to the uncharged capacitor by the closing of S 2. Calculate the initial charge acquired by C 1 and the final charge on each capacitor. Example

Solution

Quiz a b c How does the potential difference V ab between a and b compare to the potential difference V bc between b and c ? 6 V6 V 5  F 10  F A) V ab  V bc B) V ab  V bc C) V ab  V bc

Energy Stored in a Capacitor +q -q dq Remove dq from lower plate and add to upper plate: Increase in P.E., Start at q = 0, finish at q = Q:

Example What is the energy stored in a parallel-plate capacitor, in terms of the plates’ area and separation? s Area A +Q -Q

Example Calculate the energy stored in a 18μF capacitor when it is charged to a potential of 100V.

Example Three capacitors of 8μF,10μF and 14μF are connected to the terminals of a 12-volt battery. How much energy does the battery supply if the capacitors are connected a)In series b)In parallel