Question

If you want a characteristic RL time constant of 1.00 s, and you have a resistor $\mathbf{500}\mathbf{}\mathit{\Omega }$, what value of self-inductance is needed?

Short answer

The value of self-inductance is 500 H

Step-by-step solution

Given Data

The time constant of the RL circuit is $\tau =1.00s$

The value of resistance is$R=500\Omega$

Concept Introduction

The trait of a current-carrying coil that resists or opposes the change in current flowing through it is known as self-inductance. This is mostly owing to the self-induced emf generated by the coil.

Calculating the Value of Self-Inductance

In RL circuits, the time constant,$\tau$, can be expressed as,

$\tau =\frac{L}{R}$…………….(1)

Rearrange equation (1) for the self-inductance and the substitute the given data, such that

$$\begin{gathered} L=\tau R \\ L=(1.00s)\times \left(500\Omega \right) \\ =500H \end{gathered}$$

Therefore, the self-inductance is 500 H