Part B and Part D Two capacitors arc connected in a circuit in series as shown i

Question

Part B and Part D

Two capacitors arc connected in a circuit in series as shown in the figure. The capacitances arc C_1 = 5 mu F, and C_2 = 95 mu F. (a) Express the total capacitance C in terms of the two capacitances C_1 and C_2. (b) Calculate the numerical value of the total capacitance C in mu F? (c) If the battery carries a voltage of Delta V, express the total charge Q stored in the circuit in terms of capacitance C and voltage Delta V. (d) Calculate the numerical value of Q in C given Delta V= 65 V.

Explanation / Answer

here,

C1 = 5 * 10^-6 C

C2 = 9.5 * 10^-6 C

a)

as the capacitors are in series

the total capacitance , C = C1 * C2 /( C1 + C2)

b)

C= C1 * C2 /( C1 + C2)

C = 5 * 9.5 /( 5 + 9.5) uF

C = 3.28 uF

c)

the total charge stored , Q = C * dV

Q = dV * C1 * C2 /( C1 + C2)

d)

dV = 6.5 V

Q = C * dV

Q = 3.28 * 10^-6 * 6.5

Q = 2.13 * 10^-5 C

the total charge stored in the circuit is 2.13 * 10^-5 C

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