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Answer to Question #5592 in Electric Circuits for manahil

Question #5592
two capacitor of capacitance 4 microfarad are charged to the potential difference of 300 volts n 400 volts respectively they are then connected in parallel what will be the resultant potential difference &charge on each capacitor??
Expert's answer
two capacitor of capacitance 4 microfarad are charged to the potential difference of 300 volts n 400 volts respectively they are then connected in parallel what will be the resultant potential difference and charge on each capacitor??

C1 = 4μ
U1 = 300v
W1 = C1*U1²/2 = 4*300²/2 = 18*10^4 - the energy of the first condencer;

C1 = 4μ
U1 = 400v
W1 = C1*U2²/2 = 4*400²/2 = 32*10^4 - the energy of the second condencer;

We assume that capacitors are connected the similar charged plates.

C12 = C1 + C2 = 4 + 4 = 8μ - capacitance of connected capacitors;
w12 = W1 + W2 = (18+32)*10^4 = 5*10^5 - the energy of connected capacitors;
U12 = sqrt(2*W12/C12) = sqrt(2*5*10^5/8) = sqrt(10^6/8) = sqrt(125*10^3) ≈ 353.5534 V - the resultant potential difference.
Q1 = C1*U12 = 4*353.5534 = 1414.2136 - the charge on the first capacitor;
Q2 = C2*U12 = 4*353.5534 = 1414.2136 - the charge on the second capacitor.

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