Question

An inductor stores \(16\,\text{J}\) of magnetic field energy and dissipates \(32\,\text{W}\) of thermal energy due to its resistance when an alternating current of \(2\,\text{A}\) (rms) and frequency \(50\,\text{Hz}\) flows through it. The ratio of inductive reactance to resistance is _______. \((\pi=3.14)\) Given: \[ U=16\,\text{J},\quad P=32\,\text{W},\quad I=2\,\text{A},\quad f=50\,\text{Hz} \]

Hint:

Always calculate \(L\) and \(R\) separately using energy and power relations before finding reactance ratios.

Answer 1

Correct Answer: 314

Concept: Energy stored in an inductor: \[ U=\frac{1}{2}LI^2 \] Power dissipated in resistance: \[ P=I^2R \] Inductive reactance: \[ X_L=\omega L=2\pi fL \]
Step 1: Find inductance \[ 16=\frac{1}{2}L(2)^2 \Rightarrow L=8\,\text{H} \]
Step 2: Find resistance \[ 32=(2)^2R \Rightarrow R=8\,\Omega \]
Step 3: Find inductive reactance \[ X_L=2\pi fL=2\times3.14\times50\times8=2512\,\Omega \]
Step 4: Ratio \[ \frac{X_L}{R}=\frac{2512}{8}=314 \] Final Answer: \[ \boxed{314} \]