An inductor coil stores 32 J of magnetic field energy and dissipates energy as heat at the rate of 320 W when a current of 4 A is passed through it. The time constant of the circuit when this coil is joined across an ideal battery will be

Question

An inductor coil stores 32 J of magnetic field energy and dissipates energy as heat at the rate of 320 W when a current of 4 A is passed through it. The time constant of the circuit when this coil is joined across an ideal battery will be (A) 0.2 s (B) 0.3 s (C) 0.4 s (D) 0.5 s

Tardigrade Admin · Accepted Answer

We know that U=(1/2)LI2 ⇒ 32=(1/2)L(4)2 ⇒ L=4 H And power P=I2R ⇒ 320=(4)2R ⇒ R=20 Ω We know that τ=(L/R) ⇒ τ=(4/20) ⇒ τ=0.2 s

Q. An inductor coil stores $32 J$ of magnetic field energy and dissipates energy as heat at the rate of $320 W$ when a current of $4 A$ is passed through it. The time constant of the circuit when this coil is joined across an ideal battery will be

$0.2 s$

$0.3 s$

$0.4 s$

$0.5 s$

We know that $U = \frac{1}{2} L I^{2}$
$\Rightarrow 32 = \frac{1}{2} L (4)^{2}$
$\Rightarrow L = 4 H$
And power $P = I^{2} R$
$\Rightarrow 320 = (4)^{2} R$
$\Rightarrow R = 20 Ω$
We know that $τ = \frac{L}{R}$
$\Rightarrow τ = \frac{4}{20}$
$\Rightarrow τ = 0.2 s$

Q. An inductor coil stores 32J of magnetic field energy and dissipates energy as heat at the rate of 320W when a current of 4A is passed through it. The time constant of the circuit when this coil is joined across an ideal battery will be

0.2s

0.3s

0.4s

0.5s