**CUMULATIVE PROBLEM** A 12.5- F capacitor is charged to a potential of 30.0 V a
ID: 1549750 • Letter: #
Question
**CUMULATIVE PROBLEM**
A 12.5- F capacitor is charged to a potential of 30.0 V and then discharged through a 65.0 resistor.
1) How long after discharge begins does it take for the capacitor to lose 90.0% of its initial charge?
2) How long after discharge begins does it take for the capacitor to lose 90.0% of its initial energy?
3) What is the current through the resistor at the time when the capacitor has lost 90.0% of its initial charge?
4) What is the current through the resistor at the time when the capacitor has lost 90.0% of its initial energy?
Explanation / Answer
A
Q/ Qo = e ^ [-t/ (RC)]
0.9 = e ^ [-t/ (RC)]
0.9 = e ^ [-t/ (12.5*65e-6]
0.9 = e ^ (-1230.769 t)
t = 8.56*10^-5s
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B
Initial Energy stored = 0.5 * Qo²/ C
Final energy stored =( 9/10)* {0.5 * Qo²/ C) = 0.9 Q ²/C
½ Qo² = Q ²
Q/ Qo = 0.707 = e ^ (-1230.769 t)
t = 2.8171*10^-4 s
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