जब एक विधुत वाहक बल \(e = e _{0} \sin (100 t )\), जहाँ \(t\) सेकण्ड में है, के प्रत्यावर्ती स्त्रोत को एक परिपथ से जोड़ते हैं तो विधुत वाहक बल \(e\) तथा धारा \(i\) में \(\frac{\pi}{4}\) का कलान्तर पाया जाता है। निम्न में से किस परिपथ में ऐसा होगा ?

A \(RC\) परिपथ, जहाँ \(R =1 k \Omega\) तथा \(C =1 \mu F\)
B \(RL\) परिपथ, जहाँ \(R =1 k \Omega\) तथा \(L =10 mH\)
C \(RL\) परिपथ, जहाँ \(R =1 k \Omega\) तथा \(L =1 mH\)
D \(RC\) परिपथ, जहाँ \(R =1 k \Omega\) तथा \(C =10 \mu F\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(RC\) परिपथ, जहाँ \(R =1 k \Omega\) तथा \(C =10 \mu F\)

Step-by-step Solution

Detailed explanation

Given phase difference \(=\frac{\pi}{4}\) and \(\omega=100\) \(rad/s\) \(\Rightarrow\) Reactance \((X)=\) Resistance \((R)\) Now by checking option. Option \((A)\) \(\mathrm{R}=1000 \,\Omega\) and \(\mathrm{X}_{\mathrm{c}}=\frac{1}{10^{-6} \times 100}=10^{4} \,\Omega\) Option…

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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