A20.0 μf capacitor initially charged to 30.0 μc is discharged through a 1.80 kω resistor. how long does it take to reduce the capacitor's charge to 15.0 μc

The charge Q at time t on the capacitor (initially charged) in a RC-circuit is given by
(1)
where is the initial charge, and is the time constant of the circuit.

Using and we can calculate the time constant:


The problem asks for the time t at which the capacitor's charge is reduced to . Since the initial charge is , we can write

And we can rewrite equation (1) as


By solving this and by using , we find

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