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A uniformly would soleacidal (ie) of self inductance $8 \times 10^{-4}\;H$ and resistance $45\;L$ is broken into two identical coils. These colis are then connected in parallel across a battery of $10V$ of negligible resistance the time constant for this circuit is

$(a)\;4 \times 10^{-4}\;S \\ (b)\;\frac{1}{2} \times 10^{-4}\;S \\(c)\;2 \times 10^{-4}\;S \\(d)\;1 \times 10^{-4}\;S $

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1 Answer

When a srteroid is cut it two parts the self inductance and resistance will become half.
$L$ for each part $ = \large\frac{8 \times 10^{-4}}{2} $$=4 \times 10^{-4}\;H$
R for each part $=2 \Omega$
When they are connected in parallel the effective inductance $L= \large\frac{4 \times 10^{-4}}{2}$
$\qquad= 2 \times 10^{-4}\;H$
effective $R=\large\frac{2}{2}$$ \;\Omega=1 \Omega$
The time constant $T= \large\frac{L}{R}$
$\qquad= \large\frac{2 \times 10^{-4}}{1}$
$\qquad= 2 \times 10^{-4}$
Hence c is the correct answer.
answered Mar 24, 2014 by meena.p

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