\(0.5 \,mH\), ના ઈન્ડકટર, \(200 \,\mu F\) નાં સંધારક અને \(2 \,\Omega\) ના અવરોધને \(220 \,V\) \(ac\) ઉદગમ સાથે શ્રેણીમાં જોડવામાં આવેલા છે. જો પ્રવાહ એ \(emf\) સાથે કળામાં હોય તી \(ac\) ઉદગમની આવૃતિ ................ \(\times 10^{2} \,Hz\) હશે.

A \(6\)
B \(5\)
C \(4\)
D \(3\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(5\)

Step-by-step Solution

Detailed explanation

If Current is in phase with emf then the frequency of source \(=\frac{1}{2 \pi \sqrt{L C}}\) (Resonant frequency) \(\frac{1}{2 \pi \sqrt{\frac{1}{2} \times 10^{-3} \times 2 \times 10^{-4}}}\) \(=\frac{1}{2 \pi} \times \sqrt{10} \times 1000=500 \,Hz\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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