An inductor coil stores $U$ energy when $i$ current is passed through it and dissipates energy at the rate of $P$ . The time constant of the circuit, when this coil is connected across a battery of zero internal resistance is :

\frac{4 U}{P}

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\frac{U}{P}

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\frac{2 U}{P}

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\frac{2 P}{U}

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Solution

The correct option is B $\frac{2 U}{P}$
Energy stored in coil $U = \frac{1}{2} L I^{2}$

Power dissipated $P = I^{2} R$

From above equation $L = \frac{2 U}{I^{2}}, R = \frac{P}{I^{2}}$

we know that time constant $τ = \frac{L}{R} = \frac{2 U / I^{2}}{P / I^{2}}$

$τ = \frac{2 U}{P}$

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An inductor coil stores U energy when i current is passed through it and dissipates energy at the rate of P. The time constant of the circuit, when this coil is connected across a battery of zero internal resistance is :

The correct option is B 2UPEnergy stored in coil U=12LI2Power dissipated P=I2RFrom above equation L=2UI2,R=PI2we know that time constant τ=LR=2U/I2P/I2τ=2UP

An inductor coil stores $U$ energy when $i$ current is passed through it and dissipates energy at the rate of $P$ . The time constant of the circuit, when this coil is connected across a battery of zero internal resistance is :

The correct option is B $\frac{2 U}{P}$
Energy stored in coil $U = \frac{1}{2} L I^{2}$

Power dissipated $P = I^{2} R$

From above equation $L = \frac{2 U}{I^{2}}, R = \frac{P}{I^{2}}$

we know that time constant $τ = \frac{L}{R} = \frac{2 U / I^{2}}{P / I^{2}}$

$τ = \frac{2 U}{P}$