Question

In the circuit shown (figure), the coil has inductance and resistance. When $X$ is joined to $Y$, the time constant is $t$ during the growth of current.
When the steady state is reached, heat is produced in the coil at a rate $P$. $X$ is now joined to $Z$. After joining $X$ and $Z$ :

• A. The total heat produced in the coil is $P\tau$
• B. The total heat produced in the coil is $1/2P\tau$
• C. The total heat produced in the coil is $2P\tau$
• D. The data given are not sufficient to reach a conclusion

Answer 1

Answer: (B)

In steady state: $P=I^{2}R$
Energy in inductor $=\frac{1}{2}L{I}^2$
After connecting $x$ and $z$, the whole energy of inductor will go into heat so heat produced:
$H=\frac{1}{2}L{I}^2=\frac{1}{2}L\frac{P}{R}=\frac{1}{2}P\tau$