In LR circuit current increases to one fourth of its maximum value in 4,sec , then time constant of

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7.Alternating Current

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In $LR$ circuit the current increases to one fourth of its maximum value in $4\,sec$, then the time constant of the circuit is

A

$2\,log_e\,2$

B

${\mkern 1mu} \frac{4}{{lo{g_e}{\mkern 1mu} 2}}$

C

${\mkern 1mu} \frac{4}{{lo{g_e}{\mkern 1mu} \left( {\frac{4}{3}} \right)}}$

D

${\mkern 1mu} \frac{{lo{g_e}{\mkern 1mu} 2}}{2}$

Solution

$I = I_0 (1 -e^{-t/\lambda })$

$\frac {I_0}{4}= I_0 (1 -e^{-4/\lambda })$

Standard 12

Physics

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