Your roommate, also taking physics, calls from the college radio station where a

Question

Your roommate, also taking physics, calls from the college radio station where a small disaster has occurred. The transmitter has malfunctioned, and a capacitor is needed to make repairs. One cannot be obtained from the transmitter manufacturer for several days. Your roommate has fashioned a capacitor out of two sheets of metal, with area 5.0 cm^2, separated by a thin 1.0 mm sheet of glass. A voltage of 120 V is placed across the homemade capacitor.

a. Calculate the capacitance. The resistivity of the glass is rho = 1.2 x 10^13 ohms*m , and the dielectric constant is k=5.6 . Hint: Remember that I = dQ/dt.

b. Calculate amount of energy stored in the capacitor.

Explanation / Answer

Given Area , A = 5.0 cm^2 Distance of seperation , d = 1.0mm Potential difference, V = 120 V Dielectric constant, k = 5.6 a) The capacitance C = k o A /d                                   = 5.6 *(8.85 *10^-12 F/m) *(5.0 *10^-4 m^2)/ (1.0 *10^-3 m)           C = 24.7 *10^-12 F or 24.7 pF b) Energy stored in the capacitor is            E = 1/2CV^2 = 0.5 *(24.7 *10^-12 F) *(120V)^2            E = 1.77 *10^-7 J

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