Question

In the steady state condition, the rate of heat produced in a choke coil is $P$. The time constant of the choke coil is $\tau$. If now the choke coil is short circuited, then the total heat dissipated in the coil is :

• A. $P\tau$
• B. $\frac{1}{2}P\tau$
• C. $\frac{P\tau }{\ln \left(2\right)}$
• D. $P\tau \ln \left(2\right)$

Answer 1

The correct option is B $\frac{1}{2}P\tau$

$P=i_0^{2}R$
$\therefore$ $i_0^2=\frac{P}{R}$
$\tau =\frac{L}{R}$
$\therefore$ $L=\tau R$
Heat dissipated $=\frac{1}{2}L{i}_0^2$$=\frac{1}{2}\left(\tau R\right)\left(\frac{P}{R}\right)=\frac{1}{2}P\tau$