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. The emf frequency $f=50Hz$

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

Step-by-step solution

Part a) Step 1 : Given information 

We have been given that

Time period of emf is$\left(\mathrm{T}\right)=0.02\mathrm{seconds}$

We have to find emf frequency by using the voltage and current graph .

Detailed solution 

As we know,

Emf frequency is the number of oscillations in 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 been given that

Peak voltage$\left(V_{\circ }\right)=1V$

Peak current$\left({\mathrm{I}}_{\circ }\right)=2A$

We need to find out the inductance of the inductor using graph and given values .

Detailed Solution

As we know ,

Inductive Reactance ;$X_L$

$$\begin{gathered} X_L=\frac{V}{I_{max}} \\ {X}_L=\frac{1V}{2A}=0.5\Omega \end{gathered}$$

Also we know that ,$\omega$is angular frequency of current

$\omega =2\pi f=2\pi \times 50=100\pi$

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

Thus, this is the value of inductance.