Question

FIGURE EX32.24
shows voltage and current graphs for an inductor.

a. What is the Emf frequency f?

b. What is the value of the inductance L ?

Short answer

a. frequency, f is $50Hz$

b.$L=1.5915\times {10}^{-3}$H

Step-by-step solution

part a) step 1: Given information

We need to find the Emf frequency f using the given graph

part a) step 2 : Detailed solution 

As we know,

Emf frequency is the number of oscillations of voltage in one second ,

$$\begin{gathered} f=\frac{1}{T}=\frac{1}{0.02} \\ \Rightarrow f=50Hz \end{gathered}$$

part b)  step 1 : Given information 

We have to find out the inductance, L using the graph and given values

Detailed solution 

As we know that inductive reactance;

$$\begin{gathered} X_L=\frac{V_{max}}{I_{max}}=\frac{1V}{2A}=0.5\Omega \\ \Rightarrow X_L=\omega L \end{gathered}$$ where$\omega$is angular frequency of current

$$\begin{gathered} \omega =2\pi f=2\pi \times 50=100\pi \\ \Rightarrow L=\frac{X_L}{\omega }=\frac{0.5}{100\pi } \\ \Rightarrow L=1.5915\times {10}^{-3}H \end{gathered}$$