A potential difference V ab = 48.0 V is applied across the capacitor network of

Question

A potential difference Vab = 48.0 V is applied across the capacitor network of the following figure. (Figure 1)

If C1=C2=4.00F and C4=8.00F, what must the capacitance C3 be if the network is to store 2.30×103 J of electrical energy?

Part A A potential difference Vab 48.0 V is applied across the capacitor network of the following figure. (Figure 1) If G-G-4.00 pE and C,-8.00 ,AF, what must the capacitance CS be if the network is to store 2.30x10-3 J of electrical energy? Express your answer with the appropriate units. G-1 Value Units Submit Previous Answers Request Answer Figure 1 of 1 XIncorrect; Try Again; 4 attempts remaining C1 C2 Provide Feedback Next >

Explanation / Answer

here,

C1 = C2 = 4 uF

C4 = 8 uF

Vab = 48 V

C1 and C2 are in series , their equivalent capacitance , C5 = C1 * C2 / ( C1 + C2)

C5 = 4 * 4 /( 4 + 4) = 2 uF

C5 and C3 are in parallel, their equivalent capacitance , C6 = C5 + C3 = 2 uF + C3

C6 and C4 are in series , the equivalent capacitance , Ceq = C6 * C4 /( C6 + C4)

Ceq = ( 2 + C3) * 8 /( 2 + C3 + 8)

Ceq = ( 2 + C3) * 8 /( 2 + C3 + 8)

the energy stored in the circuit , U = 2.3 * 10^-3 J

0.5 * Ceq * Vab^2 = 2.3 * 10^-3 J

0.5 * ( 2 uF + C3) * 8 uF /( 2 uF + C3 + 8 uF) * 48^2 = 2.3 * 10^-3

0.5 * ( 2 * 10^-6 + C3) * 8 * 10^-6 /( 2 * 10^-6 + C3 + 8 * 10^-6) * 48^2 = 2.3 * 10^-3

solving for C3

C3 = 6.6 * 10^-7 F

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