Chapter 4, Problem 4.1HP

The current through a 0.8-H inductor is given by $i_L=\sin \left(100t+\frac{\pi }{4}\right)$ . Write the expression for thevoltage across the inductor.

To determine

The expression for the voltage across the inductor.

Answer to Problem 4.1HP

The expression for the voltage across the inductor is $80\left(100t+\frac{\pi }{4}\right)\text{V}$ .

Explanation of Solution

Calculation:

The expression for the voltage across the inductor is given by,

  $v_L=L\frac{d{i}_L}{dt}$

Substitute $\sin \left(100t+\frac{\pi }{4}\right)$ for $i_L$ and $0.8\text{H}$ for $L$ in the above equation.

  $\begin{array}{c}{v}_L=\left(0.8\text{H}\right)\frac{d\left(\sin \left(100t+\frac{\pi }{4}\right)\right)}{dt}\\ =\left(0.8\text{H}\right)\left(100\right)\left(100t+\frac{\pi }{4}\right)\\ =80\left(100t+\frac{\pi }{4}\right)\text{V}\end{array}$

Conclusion:

Therefore, the expression for the voltage across the inductor is $80\left(100t+\frac{\pi }{4}\right)\text{V}$ .