Question

In the circuit shown, the coil has inductance and resistance. When X is joined to Y, the time constant is t during growth of current. When the steady state is reached, rate of production of heat in the coil is "P" joule/sec. X is now joined to Z, and after long time of joining X to Z –

• A. The total heat produced in the coil is Pt
• B. The total heat produced in the coil is $\frac{1}{2}$ Pt
• C. The total heat produced in the coil is 2Pt
• D. The data given is not sufficient to reach a conclusion

Answer 1

Answer: (B)

The total heat produced in the coil is $\frac{1}{2}$ Pt

Answer 2

Let L and R be the inductance and the resistance of the coil respectively

Let E = e.m.f. of the cell.

t = Time constant, I₀ = E/R

P = $I_{0}^{2}$R = $\frac{E^{2}}{R}$

Energy stored in the coil = $\frac{1}{2}$ $LI_{0}^{2}$ = $\frac{1}{2}$ L $\left( \frac{E^{2}}{R^{2}} \right)$ = $\frac{1}{2}$

$\left( \frac{L}{R} \right)$ $\left( \frac{E^{2}}{R} \right)$ = $\frac{1}{2}$ tP

= total heat produced in the coil