What is the charge Q on the positive plate of the capacitor? What is the electri

Question

What is the charge Q on the positive plate of the capacitor? What is the electric potential energy stored in the capacitor? The 4.00 middot 103-nF capacitor is then disconnected from the 12.0-V battery and used to charge three uncharged capacitors, a 100.-nF capacitor, a 200.-nF capacitor, and a 300.-nF capacitor, connected in series. After charging, what is the potential difference across each of the tour capacitors? How much of the electrical energy stored in the 4.00 middot 103-nF capacitor was transferred to the other three capacitors?

Explanation / Answer

a)

Q1 = C1*V = 4*10^3*10^-9*12

Q = 48*10^-6 C

(b)

energy stored E = (1/2)*Q*V = (1/2)*48*10^-6*12 = 288*10^-6 J

(c)

v1 = v2 = v3 = v4

(Q1-Q)/C1 = Q/(C2+C3+C4)

(48-Q)/(4*10^3*10^-9) = Q/((100+200+300)*10^-9)

Q = 6.26 *10^-6 C

V' = (Q1-Q)/C1 = (48-6.26)*10^-6/(4*10^3*10^-9) = 10.435 V

(d)

E' = (1/2)*(Q1-Q)*V' = (1/2)*(48-6.26)*10^-6*10.435 = 218*10^-6 J

eneregy converted = E - E' = 10*10^-6 J

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