In the figure below, a potential difference V = 200 V is applied across a capaci
ID: 1534611 • Letter: I
Question
In the figure below, a potential difference V = 200 V is applied across a capacitor arrangement with capacitances C1 = 11.0 F, C2 = 7.00 F, and C3 = 3.00 F. Find the following values.
(a) the charge on capacitor 3
C
(b) the potential difference across capacitor 3
V
(c) the stored energy for capacitor 3
J
(d) the charge on capacitor 1
C
(e) the potential difference across capacitor 1
V
(f) the stored energy for capacitor 1
J
(g) the charge on capacitor 2
C
(h) the potential difference across capacitor 2
V
(i) the stored energy for capacitor 2
Explanation / Answer
Given data
V = 200 v, C1 = 11.0*10^-6 F, C2 = 7.0*10^-6 F, C3 = 3.0*10^-6 F
(a) charge on the capacitor C3
Q3 = C3 * V
= 3*10^-6 * 200
= 600*10^-6 F
(b) potential difference across capacitor C3
V3 = V
= 200 volt
(c) energy stored in the capacitor E3
E3 = 0.5 * C3 * V3^2
= 0.5 * 3.0*10^-6 * 200^2
= 0.060 J
(d) charge on C1 = charge on C2
C1*V1 = C2*V2
V1/V2 = C2/C1 = 7.0/11.0
Hence, V1 = (7/11)*200
= 127.27 v
V2 = 200 - 127.27
= 72.73 v
charge on C1 = C1*V1
= 11*10^-6 * 127.27
= 1399.97*10^-6 F
(e) potential difference across C1
V1 = 127.27 V
(f) energy stored in the capacitor C1
E1 = 0.5 * C1 * V1^2
= 0.5 * 11.0*10^-6 * 127.27^2
= 0.089 J
(g) charge on C2
= C2 * V2
= 7*10^-6 * 72.73
= 509.11*10^-6 F
(h) potential difference across C2
V2 = 72.73 v
(i) energy stored in the capacitor C2
E2 = 0.5 * C2 * V2^2
= 0.5 * 7*10^-6 *72.73^2
= 0.0185 J