Question

In an RL circuit, the time constant for an inductor is defined as t( torque) =R/L, where R is the resisitance and L is the inductance.

The transient time of an inductor is defined as five times the time constant . It represents the time it takes the inductor to store maximum energy in the magnetic field of the inductor. When the switich is closed, the current is increasing according to the following equation?

What is the energy dissipated as heat in the resistor?

Answer 1

Maximum enenrgy stored in the inductor is $E=Li\frac{\mathrm{d} i}{\mathrm{d} t}$

Here $\frac{\mathrm{d} i}{\mathrm{d} t} = \frac{V}{R}x\frac{t}{\tau }e^{-t/\tau }$

Iit is possible during tansient time $t=5\tau$

$t=5x\frac{L}{R}$

Therefore the energy stored is $E=\frac{V}{R}x\left ( \frac{V}{R}x5e^{-5} \right )$

   $E=5x\frac{V^{2}}{R^{2}}xe^{-5}$