ક્ષેત્રફળ \( 1.0 m^{2} \) ધરાવતું એક વાહક વર્તુળાકાર ગૂંચળું ચુંબકીય ક્ષેત્રને લંબ રૂપે મૂકેલું છે, જે \( B = \sin(100 t) \) ટેસ્લા મુજબ બદલાય છે. જો ગૂંચળાનો અવરોધ 100 \( \Omega \) હોય, તો એક આવર્તકાળમાં ગૂંચળામાં વ્યય થતી સરેરાશ ઉષ્મીય ઊર્જા ___________ J છે.

A \( \frac{\pi}{2} \)
B \( 2\pi \)
C \( \pi \)
D \( \pi^{2} \)

Verified Solution

Answer & Solution

Correct Answer

(C) \( \pi \)

Step-by-step Solution

Detailed explanation

ગૂંચળાનું ક્ષેત્રફળ \(=1 m^2\) \(B=\sin (100 t)\) \(\therefore \quad \phi= BA =\sin (100 t )\) \(\therefore \quad \frac{ d \phi}{ dt }=100 \cos (100 t )\) \(\therefore \quad P=\frac{V^2}{R}=\frac{10^4 \cos ^2(100 t)}{100}\) \(\therefore \quad\) 1 આવર્તકાળમાં વ્યય થતી ઉષ્મીય…

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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