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A capacitor of 1.0 mu F is connected to ...

A capacitor of `1.0 mu F` is connected to series with a resistance of `10^(4) ohm`, and a battery of 2.0 V. Find the maximum value of current and current after 0.02 s.

Text Solution

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Here, `C = 1.0 mu F = 10^(-6) F`,
`R = 10^(4) ohm, E_(0) = 2.0` volt
During charging of the condenser,
`q = q_(0) (1 - e^(-t//RC))`
`I = - I_(0) e^(-t//RC)`, where
`I_(0) = (E)/(R ) = (2.0)/(10^(4)) = 2.0 xx 10^(-4) amp`
At `t = 0.02 s, I = I_(0) (e^(-0.02//10^(4) xx 10^(-6)))`
`= 2 xx 10^(-4) e^(-2)`
`= (2 xx 10^(-4))/(e^(2)) = (2 xx 10^(-4))/((2.718)^(2)) = 0.27 xx 10^(-4) A`
`I = 27 xx 10^(-6) A = 27 mu A`
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