A 1000 V battery, a 3000 ohm resistor and a 0.5 microFarad capacitor are connect

Question

A 1000 V battery, a 3000 ohm resistor and a 0.5 microFarad capacitor are connected in series with a switch. The capacitor is initally uncharged. How long does it take for the charge on the capacitor to reach 50% of its final value? Picture below, please help! Thanks

A 1000 V battery, a 3000 ohm resistor and a 0.5 microFarad capacitor are connected in series with a switch. The capacitor is initally uncharged. How long does it take for the charge on the capacitor to reach 50% of its final value? Picture below, please help! Thanks

Explanation / Answer

time constant t = RC = 3000*0.5 uF = 1.5 ms

Q = Q0 (1-e^-t/RC)

1-e^-t/Rc = 0.5

e^-t/RC = 0.5

-t/RC = -0.693

t = 0.693 *1.5 = 1.039 ms

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