Energy stored in Capacitors?

Question

Suppose you have 3 capacitors (2uF, 4uF, 6uF). What is the ratio of the energy that can be stored in the 2uF and 4uF capacitor when they are connected in series to a 12V battery? in parallel?

Answer 1

Energy is proportional to capacitance when connected in parallel to the same voltage source. So energy stored by 4uF is twicw that of 2uF and that of 6uF is three times that of 2 uF.
When connected in series all of them store the same charge q = V C(eq); C(eq) = 1/[1/2+1/4+1/6] = 12 /11 uF so q = 12V/11
The energy stored by 2uF would be (1/2q)(q/2). This shows that 2uF will store three times more energy thn 6 uF and 4 uuF will store 1/2 of what 2u F stores.
So in first case energy stored would be 1:2:3 and in seriescase 3:2:1. It also follows from the expression for energy, 1/2) Cv^2, (1/2) (Q^2)/C and (1/2)QV

Answer 2

The energy stored in a capacitor is given by the equation

E = 1/2*C*V^2

I am confused as to why you have three capacitors (you don't use the 6 uF one in the problem). Oh well ...

The parallel circuit is the easy question. Since the voltage across each capacitor is equal, we can determine the ratio as follows.

E_4/E_2 = 1/2*4 F*12^2/1/2*2 F*12^2 = 4/2 = 2

The ratio of the energy in the capacitors equals the ratio of the capacitances.

The series connection is a bit more interesting. Let's show you how to determine the voltages across each capacitor. When the capacitors are connected to the battery, each capacitor will conduct for a time the same current since they are in series. Thus, we know that each capacitor contains the same charge. We can now right the following equations.

V_4F+V_2F=12 (Kirchoff's law)
4 F*V_4F=2 F*V_2F (each cap has the same charge)

where V_4F is the voltage across the 4 F cap
V_2F is the voltage across the 2 F cap

We can solve these two equations for the capacitor voltages to get

V_4F=4 V
V_2F = 8 V

The energy ratio is given by

E_4/E_2 = 1/2*4 F*4^2/1/2*2 F*8^2 = (4/2)*(16/64)
= 2*1/4 = 1/2
E_4/E_2 = 1/2

The energy ratio for the series circuit is the reciprocal of the energy ratio for the parallel circuit.

Answer 3

6uf Capacitor

Answer 4

The following three formulae can be used for energy stored.

0.5 CV^2, 0.5 Q^2/C and 0.5QV


IN SERIES, all capacitors have the SAME charge Q

Using the equation 0.5 Q^2/C for energy stored and noting that 0.5 & Q are constants.

The ratio of energy stored is equal to 1/C1:1/C2:1/C3



IN PARALLEL, all capacitors have the SAME potential difference V

Using the equation 0.5 CV^2for energy stored and noting that 0.5 & V are constants.

The ratio of energy stored is equal to C1:C2:C3.