Question

An inductor used in a dc power supply has an inductance of $\mathbf{12}\mathit{H}$and a resistance of $\mathbf{180}\mathbf{\Omega }$. It carries a current of $\mathbf{0}\mathbf{.}\mathbf{5}\mathbf{}\mathit{A}$. (a) What is the energy stored in the magnetic field? (b) At what rate is thermal energy developed in the inductor? (c) Does your answer to part (b) mean that the magnetic-field energy is decreasing with time? Explain.

Short answer

(a) $\mathrm{U}=1.5J$

(b) $P=45W$

(c) No

Step-by-step solution

Formula of heat energy and power in an inductor

The stored magnetic field energy in an inductor is given by $\frac{\mathbf{1}}{\mathbf{2}}\mathit{L}{\mathit{I}}^{\mathbf{2}}$.

The rate of thermal energy developed in an inductor is given by ${\mathit{I}}^{\mathbf{2}}\mathbf{}\mathit{R}$.

Calculate the energy and rate of energy development

Given that $L=12H,R=180\Omega andI=0.5A$.

The stored magnetic field energy is given by

$$\begin{gathered} U=\frac{1}{2}L{I}^2 \\ U=\frac{1}{2}x12x0.5^2 \\ U=1.5J \end{gathered}$$

The rate of development of energy is given by

$$\begin{gathered} P=I^{2}R \\ P=0.5^{2}x180 \\ P=45W \end{gathered}$$

Since the current is constant, the stored energy in the inductor is constant, where the consumed energy by the resistance of the inductor comes from the EMF source. The EMF source keeps the current constant. Hence, the magnetic field energy is not decreasing with the time.