Question

Suppose you have a 9.00 V battery, a 2.2 μF capacitor, and a 8.25 μF capacitor.

a) Find the total charge stored in the system if the capacitors are connected to the battery in series in C.

b) Find the energy stored in the system if the capacitors are connected to the battery in series in J.

c) Find the charge if the capacitors are connected to the battery in parallel in C.

d) Find the energy stored if the capacitors are connected to the battery in parallel in J.

Answer 1

Equivalent capacitance in series:

1/C_{​​​​​eq} = 1/C_{​​​​​​1} + 1/C_{​​​​​​2}

Therefore, C_{​​​​​eq} = C_{​​​​​​1}*C_{​​​​​​2}/(C_{​​​​​​1} + C_{​​​​​​2}) = 2.2*8.25/(2.2+8.25) = 1.736 F

Now,

a) total charge stored (Q) = C_{​​​​​​eq}*V = 1.74*9 = 15.63 C

b) total energy stored (E) = (0.5)*C_{​​​​​​eq}*V^{​​​​​​2} = (0.5)*1.736*9² = 70.34 J

Equivalent capacitance in parallel,

C_{​​​​​​eq} = C_{​​​​​​1} + C_{​​​​​​2}

C_{​​​​​​eq} = 2.2 + 8.25 = 10.45F

c) charge flown from the battery (Q) = C_{​​​​​​eq}*V = 10.45*9 = 94.05 C

d) total energy stored in the capacitors (E) = (0.5)*C_{​​​​​​eq}*V^{​​​​​​2} = (0.5)*10.45*9² = 423.22 J