Three capacitors arc connected as shown in the figure. C_1 = 7.8 mu F, C_2 = 12.

Question

Three capacitors arc connected as shown in the figure. C_1 = 7.8 mu F, C_2 = 12.8 mu F, C_3 = 5.1 mu F. The voltage on the battery is 12 V. (a) Express the equivalent capacitance of the two capacitors C_1 and C_2 in terms of the variables given in the problem statement. (b) Using the above result, express the total capacitance in terms of C_12 and C_3. (c) Calculate the numerical value of the total capacitance in mu F. (d) Express the charge Q stored in the circuit in terms of capacitance C and the potential difference Delta V across the battery. (e) Calculate the numerical value of Q in mu C. (f) Express the energy stored in a capacitor in terms of capacitance C and the potential difference Delta V. (g) Calculate the numerical value of U in mu J.

Explanation / Answer

(a)

from the circuit C1 and C2 are connected in paralel

C12 = C1 + C2

(b)

C12 and C3 are in series

1/ C total = 1/C12 + 1/C3

(c)

Ctotal = C12 * C3/C12 + C3

C12 = C1 +C2 = 7.8+ 12.8 = 20.6 uF

Ctotal = 20.6(5.1)/20.6 + 5.1 = 4.087 uF

(d)

Q= Ctotal * V

e) Q = 4.087 uF ( 12) = 49.05 uC

f)

U = 1/2 * C total V^2

g)

U = 1/2 * (4.087 * 10^-6) ( 12)^2

=294.264 uJ

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