Medium
$A$ series $LCR$ circuit with inductance $L = 10\,H$,capacitance $C = 10\,\mu F$,and resistance $R = 50\,\Omega$ is connected to an $AC$ source of voltage $V = 200 \sin(100t)\,V$. If the resonant frequency of the $LCR$ circuit is $\nu_{0}$ and the frequency of the $AC$ source is $\nu$,then:
- A$\nu_{0} = \nu = \frac{50}{\pi}\,Hz$
- B$\nu_{0} = \frac{50}{\pi}\,Hz, \nu = 50\,Hz$
- C$\nu = 100\,Hz; \nu_{0} = \frac{100}{\pi}\,Hz$
- D$\nu_{0} = \nu = 50\,Hz$
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Similar Questions
Match List-$I$ with List-$II$ :
List-$I$ List-$II$ $(a)$ $\omega L > \frac{1}{\omega C}$ $(i)$ Current is in phase with $emf$ $(b)$ $\omega L = \frac{1}{\omega C}$ $(ii)$ Current lags behind the applied $emf$ $(c)$ $\omega L < \frac{1}{\omega C}$ $(iii)$ Maximum current occurs $(d)$ Resonant frequency $(iv)$ Current leads the $emf$
Choose the correct answer from the options given below :
| List-$I$ | List-$II$ |
| $(a)$ $\omega L > \frac{1}{\omega C}$ | $(i)$ Current is in phase with $emf$ |
| $(b)$ $\omega L = \frac{1}{\omega C}$ | $(ii)$ Current lags behind the applied $emf$ |
| $(c)$ $\omega L < \frac{1}{\omega C}$ | $(iii)$ Maximum current occurs |
| $(d)$ Resonant frequency | $(iv)$ Current leads the $emf$ |
Choose the correct answer from the options given below :
$A$ series $L-C-R$ circuit containing a resistance $R$ has angular frequency $\omega$. At resonance,the voltages across the resistance and the inductor are $V_R$ and $V_L$ respectively. The value of the capacitance is:
The frequency at resonance for the circuit shown in the figure is:
The self-inductance of the motor of an electric fan is $10\;H$. In order to impart maximum power at $50\;Hz$, it should be connected to a capacitance (in $\mu F$) of:
MediumAIEEE 2005
View SolutionAn $LCR$ series circuit with $100 \Omega$ resistance is connected to an $AC$ source of $200 V$ and angular frequency $300 \text{ rad/s}$. When only the capacitor is removed,the current lags behind the voltage by $60^{\circ}$. When only the inductor is removed,the current leads the voltage by $60^{\circ}$. The power dissipated in the $LCR$ circuit will be:
Difficult
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