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A capacitor of capacitance 0.5 mu F is d...

A capacitor of capacitance `0.5 mu F` is discharged through a resistance. Find the value of resistance if half the charge on capacitor escapes in one minute.

Text Solution

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Hene, `C 0.5 mu F = 0.5 xx 10^(-6) F, R = ?`
`q = (q_(0))/(2), t = 1 min. = 60 sec`.
As `q = q_(0) e^(-t//RC) :. (q_(0))/(2) = q_(0) e^(-60 // RC)`
`log_(e) 1 - log_(e) 2 = - (60)/(RC) log_(e) e`
`0 - 2.303 log_(10) 2 = - (60)/(RC) xx 1`
`2.303 xx 0.3010 = (60)/(R(0.5 xx 10^(-6)))`
`:. R = (60)/(0.5 xx 10^(-6) xx 2.303 xx 0.3010)`
` = 1.73 xx 10^(8) ohm`
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