| In an a.c. circuit, the instantaneous e.m.f. and current are given by |
| \[\text{e=100 sin 30 t}\] |
| \[\text{i=20 sin }\left( 30t-\frac{\pi }{4} \right)\] |
| In one cycle of a.c., the average power consumed by the circuit and the wattles current are, respectively: |
| [JEE Main Online 08-04-2018] |
A) \[\frac{50}{\sqrt{2}},0\]
B) \[50,\,\,0\]
C) \[50,\,\,10\]
D) \[\frac{1000}{\sqrt{2}},\,\,10\]
Correct Answer: D
Solution :
| [d] \[e=100\sin (30t)\] |
| \[i=20\sin \left( 30t-\frac{\pi }{4} \right)\] |
| \[{{e}_{rms}}=\frac{100}{\sqrt{2}}volt,\] \[{{i}_{rms}}=\frac{20}{\sqrt{2}}amp\] |
| Power factor \[=\cos \phi =cos\left( -\frac{\pi }{4} \right)=\frac{1}{\sqrt{2}}\] |
| \[<P>={{e}_{rms}}{{i}_{rms}}\cos \phi \] |
| \[=\frac{100}{\sqrt{2}}\times \frac{20}{\sqrt{2}}\times \frac{1}{\sqrt{2}}\] |
| \[=\frac{1000}{\sqrt{2}}watt\] |
| Wattles current\[={{i}_{rms}}\sin \phi \] |
| \[=\frac{20}{\sqrt{2}}\times \frac{1}{\sqrt{2}}=10amp\] |
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