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GUJCET · Physics · Alternating Current
An alternating voltage of \(\mathrm{V}=\mathrm{V}_{0} \sin \omega t\) is applied across a circuit．As a result，a current \(I=I_{0} \sin \left(\omega t-\frac{\pi}{2}\right)\) flows in it. The power consumed per cycle is ____________ ．
- A \(1.919 \mathrm{~V}_{0} \mathrm{I}_{0}\) watt
- B 0 watt
- C \(0.5 \mathrm{~V}_{0} \mathrm{I}_{0}\) watt
- D \(0.707 \mathrm{~V}_{0} \mathrm{I}_{0}\) watt
Answer & Solution
Correct Answer
(B) 0 watt
Step-by-step Solution
Detailed explanation
(B) 0 watt
power \(\mathrm{P}=\frac{\mathrm{V}_{0} \mathrm{I}_{0}}{\mathrm{~V}_{0}^{2} \mathrm{I}_{0}} \cos \phi\)
\(\therefore \quad \mathrm{P}=\frac{\mathrm{V}_{0}^{2} \mathrm{I}_{0}}{2} \cos \frac{\pi}{2}\)
\(\therefore \quad \mathrm{P}=0 \quad\left(\because \cos \frac{\pi}{2}=0\right)\)
power \(\mathrm{P}=\frac{\mathrm{V}_{0} \mathrm{I}_{0}}{\mathrm{~V}_{0}^{2} \mathrm{I}_{0}} \cos \phi\)
\(\therefore \quad \mathrm{P}=\frac{\mathrm{V}_{0}^{2} \mathrm{I}_{0}}{2} \cos \frac{\pi}{2}\)
\(\therefore \quad \mathrm{P}=0 \quad\left(\because \cos \frac{\pi}{2}=0\right)\)
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