(D) In a parallel $LC$ circuit,the total impedance $Z$ is given by $\frac{1}{Z} = \sqrt{(\frac{1}{X_L} - \frac{1}{X_C})^2}$.At resonance,$\omega^2 = \

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voltage is maximum when $\omega^2 = \frac{1}{LC}$

(D) In a parallel $LC$ circuit,the total impedance $Z$ is given by $\frac{1}{Z} = \sqrt{(\frac{1}{X_L} - \frac{1}{X_C})^2}$.At resonance,$\omega^2 = \frac{1}{LC}$,which implies $X_L = X_C$.At this frequency,the net current drawn from the source is minimum because the impedance $Z$ becomes infinite.Since the circuit is connected in parallel,the voltage across the inductance $L$ and capacitance $C$ is the same as the source voltage.However,in a parallel $LC$ circuit at resonance,the circulating current between $L$ and $C$ is maximum,leading to maximum voltage across the components.

Class 12 Physics Alternating Current Inductance, Capacitance and Resistance in Series and Parallel

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An alternating voltage of frequency $\omega$ is induced in an electric circuit consisting of an inductance $L$ and capacitance $C$,connected in parallel. Then across the inductance coil:

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A
current is maximum when $\omega^2 = \frac{1}{LC}$
B
current is zero
C
voltage is minimum when $\omega^2 = \frac{1}{LC}$
D
voltage is maximum when $\omega^2 = \frac{1}{LC}$

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Alternating Current

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Inductance, Capacitance and Resistance in Series and Parallel

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As shown in the figure,a series circuit connected across a $200 \,V, 60 \,Hz$ line consists of a capacitor of capacitive reactance $X_C = 30 \,\Omega$,a non-inductive resistor of $R_1 = 44 \,\Omega$,and a coil of inductive reactance $X_L = 90 \,\Omega$ and resistance $R_2 = 36 \,\Omega$. The power dissipated in the coil is.....$W$

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An $L-C-R$ series circuit is connected to an $AC$ source of peak voltage $240 \ V$. The phase difference between voltage and current of this circuit is $45^{\circ}$ and the resistance is $100 \ \Omega$. The $rms$ value of current through the circuit is . . . . . . . (in $A$)

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In the adjoining figure,the impedance of the circuit will be $... \Omega$.

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An $LCR$ series circuit with $R = 100\,\Omega$ is connected to a $200\,V, 50\,Hz$ $a.c.$ source. When only the capacitance is removed,the current lags the voltage by $60^o$. When only the inductance is removed,the current leads the voltage by $60^o$. The current in the circuit is.....$A$

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The angular frequency of alternating current in an $L-C-R$ circuit is $100 \, rad/s$. The components connected are shown in the figure. Find the value of the inductance of the coil and the capacity of the condenser.

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An alternating voltage of frequency $\omega$ is induced in an electric circuit consisting of an inductance $L$ and capacitance $C$,connected in parallel. Then across the inductance coil:

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An $L-C-R$ series circuit is connected to an $AC$ source of peak voltage $240 \ V$. The phase difference between voltage and current of this circuit is $45^{\circ}$ and the resistance is $100 \ \Omega$. The $rms$ value of current through the circuit is . . . . . . . (in $A$)

In the adjoining figure,the impedance of the circuit will be $... \Omega$.

An $LCR$ series circuit with $R = 100\,\Omega$ is connected to a $200\,V, 50\,Hz$ $a.c.$ source. When only the capacitance is removed,the current lags the voltage by $60^o$. When only the inductance is removed,the current leads the voltage by $60^o$. The current in the circuit is.....$A$

The angular frequency of alternating current in an $L-C-R$ circuit is $100 \, rad/s$. The components connected are shown in the figure. Find the value of the inductance of the coil and the capacity of the condenser.

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