Question

An inductor is connected to a $15kHz$oscillator. The peak current is $65mA$ when the rms voltage is $6.0V$. What is the value of the inductance L?

Short answer

The value of Inductance is$L=1.38mH$

Step-by-step solution

Given information 

We have been given that

Frequency of oscillator is $\left(f\right)=15KHz$

Value of peak current $\left({\mathrm{I}}_{\circ }\right)=65mA$

RMS Voltage$\left(V_{rms}\right)=6.0V$

We need to find out the inductance of an inductor connected to an oscillator

Detailed solution 

As we know that Inductive Reactance; $X_L=2\pi fL$where f is frequency of oscillator and L is inductance

$\Rightarrow L=\frac{X_L}{2\pi f}......\left(1\right)$

Also,

$$\begin{gathered} X_L=\frac{V_{max}}{I_{max}} \\ \Rightarrow X_L=\frac{\sqrt{2}{V}_{rms}}{I_{max}}......\left(2\right) \end{gathered}$$where $V_{rms}=6V;I_{max}=65mA$

On Putting (2) in (1) we get,

localid="1649880677194" width="356">L=2VrmsImax(2πf)=2×665×10-3×2×3.14×15×1000L=1.38mH