એક પરિપથમાં \(V = V _0 \sin \omega t\) વડે અપાતો એક ઓલ્ટરનેટિંગ વોલ્ટેજ લાગુ પાડતાં પરિપથમાં મળતો પ્રવાહ \(I=I_0 \sin \left(\omega t-\frac{\pi}{2}\right)\) છે. પરિપથમાં વપરાતો પાવર __________.

A \(1.919 V_0 I _0\) વોટ
B 0 વોટ
C \(0.5 V_0 I _0\) વોટ
D \(0.707 V_0 I _0\) વોટ

Verified Solution

Answer & Solution

Correct Answer

(B) 0 વોટ

Step-by-step Solution

Detailed explanation

B.0 વોટ
આપેલ વોલ્ટેજ અને પ્રવાહના સૂત્ર
પરથી, \(\phi=\frac{\pi}{2}\)
પાવર \(P =\frac{ V _0 I _0}{2} \cos \phi\)
\(\therefore \quad P =-\frac{ V _0 I _0}{2} \cos \frac{\pi}{2}\)
\(\therefore \quad P=0 \quad\left(\because \cos \frac{\pi}{2}=0\right)\)

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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