| Directions : (41-45) |
| Power Associated with LCR Circuit |
| In an a.c. circuit, values of voltage and current change every instant. Therefore power of an a.c. circuit at any instant is the product of instantaneous voltage (E) and instantaneous current (I). The average power supplied to a pure resistance R over a complete cycle of a.c. is \[P={{E}_{v}}{{I}_{v}}\], when circuit is inductive, average power per cycle is \[{{E}_{v}}{{I}_{v}}\cos \phi \]. |
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| In an a.c. circuit, 600 mH inductor and a \[50\mu F\] capacitor are connected in series with \[10\Omega \] resistance. The a.c.c supply to the circuit is 230 V, 60 Hz. |
A) \[10\centerdot 42W\]
B) \[15\centerdot 25W\]
C) \[17\centerdot 42W\]
D) \[13\centerdot 45W.\]
Correct Answer: C
Solution :
Average power transferred per cycle to resistance is \[{{P}_{v}}=I_{v}^{2}R\] As \[{{X}_{L}}=\omega L=2\pi vL=2\times \frac{22}{7}\times 60\times 0.6=226.28\Omega \] \[{{X}_{C}}=\frac{1}{\omega C}=\frac{1}{2\pi vC}=\frac{1}{2\times 22/7\times 60\times 50\times {{10}^{-6}}}\] \[=53\,.\,03\,\Omega \] \[Z=\sqrt{{{R}^{2}}+{{\left( {{X}_{L}}-{{X}_{C}} \right)}^{2}}}\] \[=\sqrt{{{\left( 10 \right)}^{2}}+{{\left( 226\,.\,28-53\,.\,03 \right)}^{2}}}=173\,.\,53\,\Omega \] \[{{I}_{v}}=\frac{{{E}_{v}}}{Z}=\frac{230}{173\,.\,53}=13\,.\,2\,A\] \[{{P}_{V}}=I_{v}^{2}R={{\left( 1.32 \right)}^{2}}\times 10=17\,.\,42\,W\]
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