Question:
An inductance of negligible resistance, whose reactance is \(120\) \(\Omega\) at \(200\) Hz is connected to a \(240\) V, \(60\) Hz Power line. The current in the inductor is
An inductance of negligible resistance, whose reactance is \(120\) \(\Omega\) at \(200\) Hz is connected to a \(240\) V, \(60\) Hz Power line. The current in the inductor is
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Inductive reactance is proportional to frequency. Find the reactance at 60 Hz and apply Ohm's law.
Updated On: Nov 12, 2026
- \(6.66\) A
- \(6.60\) A
- \(5.45\) A
- \(54.5\) A
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept
Inductive reactance is \(X_L=2\pi fL\), so \(X_L\propto f\).
Step 2: Reactance at 60 Hz
\(X_L'=120\times\dfrac{60}{200}=36\ \Omega\).
Step 3: Current
With negligible resistance, \(I=\dfrac{V}{X_L'}=\dfrac{240}{36}\).
Step 4: Result
\(I\approx6.66\) A.
Final Answer:
The current in the inductor is about 6.66 A. \[ \boxed{\text{(A) }6.66\text{ A}} \]
Inductive reactance is \(X_L=2\pi fL\), so \(X_L\propto f\).
Step 2: Reactance at 60 Hz
\(X_L'=120\times\dfrac{60}{200}=36\ \Omega\).
Step 3: Current
With negligible resistance, \(I=\dfrac{V}{X_L'}=\dfrac{240}{36}\).
Step 4: Result
\(I\approx6.66\) A.
Final Answer:
The current in the inductor is about 6.66 A. \[ \boxed{\text{(A) }6.66\text{ A}} \]
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