A 2.0-?F capacitor is charged to 12 V and then discharged through a 4.0 × 106 ? resistor. How...
A 2.0-µF capacitor is charged to 12V and then discharged through a 4.0 × 106 O resistor. How long will it take for the voltage across the capacitor to drop to 3.0V?
a) 22 s
b) 8.0 s
c) 11 s
d) 24 s
e) 4.5 s
Homework Answers
given that
capacitence of capacitor =C = 2.0μF = 2.0 *10-6 F
intial voltage = Vo = 12v
resistance = R = 4 * 106 Ω
final voltage = V = 3v
from the equation in the RC circuit dischrging
q = q0e-t/RC
but q = CV
so CV =CVo e-t/RC
V = Vo e-t/RC
3v = 12v e-t/RC
taking natural logartims on both sides
-t/RC = ln(3v/12v)
t = -RC ln(3v/12v)
=- 4 * 106 Ω * 2 * 10-6 Fln(3v/12v) =11s
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