14. +0/10 points | Previous Answers Tipler6 24.P.032 My Notes For the circuit sh

Question

14. +0/10 points | Previous Answers Tipler6 24.P.032 My Notes For the circuit shown in the figure below, the capacitors were each discharged before being connected to the voltage source V=194 V 4.0 F 12.0 F 1 15.011 F (a) Find the equivalent capacitance of the combination 12.36 (b) Find the charge stored on the positively charged plate of each capacitor. 15.0 F capacitor | 4.0 F capacitor 12.0 F capacitor (c) Find the voltage across each capacitor 15.0 F capacitor 4.0 F capacitor 12.0 F capacitor (d) Find the energy stored in each capacitor 15.0 F capacitor 4.0 F capacitor 12.0 F capacitor mJ mJ mJ

Explanation / Answer

Let's consider 15 uF = C1 , 4 uF = C2 and 12 uF = C3.

(a)

Capacitors 15 uF and 4 uF are in series combination.

C12 = 1 / C1 + 1 / C2

C12 = 1 / 15uF + 1 / 4uF

C12 = 3.16 uF

This is parallel with with 12 uF capacitor.

Ceq = 3.16 + 12

Ceq = 15.16 uF

(b)

We know that charge is same in series combination and voltage is same in parallel .

Q12 = V*C12

Q12 = 194 * 3.16 = 613.04 uC

Q1 = Q2 = 613.04 uC

V3 = V = 194 V

Q3 = C3*V3 = 12uF * 194

Q3 = 2328 uC

(c)

V1 = Q1 / C1 = 613.04 / 15

V1 = 40.86 V

V2 = 613.04 / 4

V2 = 153.26 V

V3 = 194 V

(d)

U1 = (1/2)C1V1^2 = (1/2)*15u * (40.86)^2

U1 = 12.52 mJ

U2 = (1/2)C2V2^2 = (1/2)*4u*(153.26)^2

U2 = 46.97 mJ

U3 = (1/2)*C3*V3^2 = (1/2)*12u*194^2

U3 = 225.81 mJ

Answer

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