A cube of gold (initially at a temperature of 21.7°C) that is 2.90 mm on a side
ID: 1694066 • Letter: A
Question
A cube of gold (initially at a temperature of 21.7°C) that is 2.90 mm on a side is connected across the terminals of a 25.0-µF capacitor that initially has a potential difference of 120.0 V between its plates. a) What time is required to fully discharge the capacitor? The capacitor is fully discharged when the charge is less than 0.01 % which roughly corresponds to a time of 10t. a) What time is required to fully discharge the capacitor? The capacitor is fully discharged when the charge is less than 0.01 % which roughly corresponds to a time of 10t.
Explanation / Answer
Let p be resistivity of gold = 2.44 uohm-cm at 20 deg C Let a be the coefficient of resistivity = .0034 p = 1.44 *(1 + .0034 * 1.7) * 10E-6 ohm-cm = 2.45 * 10E-6 ohm-cm R = p L / A = 2.45 * 10E-6 * .29 / .29^2 = 8.46 * 10E-6 ohms Q = Q0 e^-t/(RC) ln Q/Q0 = ln .01 = -t/(RC) t = -RC * ln .01 = 9.74 * 10E-10 sec
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