| Directions : (16-20) |
| Average Power Associated with an inductor and Capacitor |
| The power averaged over one full cycle of a.c. is known as average power. It is also known as true power. |
| \[{{P}_{av}}={{V}_{rms}}\,{{I}_{rms}}\cos \phi =\frac{{{V}_{0}}{{I}_{0}}}{2}\,\cos \phi \] |
| Root mean square or simply rms watts refer to continuous power. |
| A circuit containing a 80 mH inductor and a \[60\,\mu F\] capacitor in series is connected to a 230 V, 50 Hz supply. The resistance of the circuit is negligible. |
 |
A) 15 A
B) \[11\centerdot 63A\]
C) \[17\centerdot 65A\]
D) \[6\centerdot 33A\]
Correct Answer: B
Solution :
Inductanc, \[L=80\,mH=80\times {{10}^{-3}}\,H\] Capacitance,\[C=60\mu F=60\times {{10}^{-6}}F,\,V=230\,V\] Frequency, \[v=50\,\,Hz\] \[\omega =2\pi v=100\pi \,\,rad\,{{s}^{-1}}\] Peak voltage, \[{{V}_{0}}=V\sqrt{2}=230\sqrt{2}\,V\] Maximm current is given by, \[{{I}_{0}}=\frac{230\sqrt{2}}{\left( 100\pi \times 80\times {{10}^{-3}}-\frac{1}{100\pi \times 60\times {{10}^{-6}}} \right)}\] \[{{I}_{0}}=\frac{230\sqrt{2}}{\left( 8\pi \times \frac{1000}{6\pi } \right)}=-11.63\,A\] Amplitude of maximum current, \[{{I}_{0}}=11.63\,A\]
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