એક AC જનરેટરમાં, \(t =0\) સમયે પ્રેરિત \(\operatorname{emf} \varepsilon=0\) હોય, તો તેનું મૂલ્ય ___________ હોય છે.

A \(t = \frac{2 \pi}{3 \omega}\) સમયે લઘુત્તમ
B \(t = \frac{\pi}{2 \omega}\) સમયે લઘુત્તમ
C \(t = \frac{2 \pi}{\omega}\) સમયે મહત્તમ
D \(t = \frac{\pi}{2 \omega}\) સમયે મહત્તમ

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Answer & Solution

Correct Answer

(D) \(t = \frac{\pi}{2 \omega}\) સમયે મહત્તમ

Step-by-step Solution

Detailed explanation

આપેલ છે કે \(t=0\) સમયે \(\varepsilon=0\), પ્રેરિત emf \(\varepsilon = \varepsilon_0 \sin(\omega t)\) છે. જ્યારે \(\sin(\omega t) = 1\) હોય ત્યારે emf મહત્તમ હોય છે.

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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