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A capacitor with initial charge q0 is discharged through a resistor. What multiple of the time constant τ gives the time the capacitor takes to lose (a) the first 1/5-th of its charge and (b)4/5-th of its charge?

Question

A capacitor with initial charge q0 is discharged through a resistor. What multiple of the time constant τ gives the time the capacitor takes to lose (a) the first 1/5-th of its charge and (b)4/5-th of its charge?

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Step 1

Charge is given by,

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Step 2

(a)

When the capacitor loses one-fifth of the charge,

q(t)0
5
4go
goe
t =0.22
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q(t)0 5 4go goe t =0.22

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Step 3

(b)

When the capacitor loses four...

4go
q(t)
oe
t =1.61r
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4go q(t) oe t =1.61r

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