(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

Medium

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:

MHT CET 2023 All MHT CET

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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If a resistance of $100\, \Omega$,an inductance of $0.5\, H$,and a capacitance of $10 \times 10^{-6}\, F$ are connected in series to a $50\, Hz$ $AC$ supply,then the impedance is:

Medium

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$A$ capacitor,an inductor,and an electric bulb are connected in series to an a.c. supply of variable frequency. As the frequency of the supply is increased gradually,the electric bulb is found to

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In an $LCR$ series circuit, if the potential differences across the inductor, capacitor, and resistor are $60 \,V$, $30 \,V$, and $40 \,V$ respectively, then the $AC$ voltage applied to the circuit is: (in $\,V$)

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Study the circuits $(a)$ and $(b)$ shown in the figure and answer the following questions.
$(a)$ Under which conditions would the $rms$ currents in the two circuits be the same?
$(b)$ Can the $rms$ current in circuit $(b)$ be larger than that in $(a)$?

Medium

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In an $LCR$ series circuit,if the angular frequency $\omega$ is gradually increased,then match the following columns:
Column-$I$ Column-$II$
$(A)$ Capacitive reactance $(i)$ Will continuously increase
$(B)$ Inductive reactance (ii) Will remain constant
$(C)$ Resistance (iii) Will first decrease and then increase
$(D)$ Total impedance (iv) Will continuously decrease

Column-$I$	Column-$II$
$(A)$ Capacitive reactance	$(i)$ Will continuously increase
$(B)$ Inductive reactance	(ii) Will remain constant
$(C)$ Resistance	(iii) Will first decrease and then increase
$(D)$ Total impedance	(iv) Will continuously decrease

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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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If a resistance of $100\, \Omega$,an inductance of $0.5\, H$,and a capacitance of $10 \times 10^{-6}\, F$ are connected in series to a $50\, Hz$ $AC$ supply,then the impedance is:

$A$ capacitor,an inductor,and an electric bulb are connected in series to an a.c. supply of variable frequency. As the frequency of the supply is increased gradually,the electric bulb is found to

In an $LCR$ series circuit, if the potential differences across the inductor, capacitor, and resistor are $60 \,V$, $30 \,V$, and $40 \,V$ respectively, then the $AC$ voltage applied to the circuit is: (in $\,V$)

Study the circuits $(a)$ and $(b)$ shown in the figure and answer the following questions.$(a)$ Under which conditions would the $rms$ currents in the two circuits be the same?$(b)$ Can the $rms$ current in circuit $(b)$ be larger than that in $(a)$?

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Study the circuits $(a)$ and $(b)$ shown in the figure and answer the following questions.
$(a)$ Under which conditions would the $rms$ currents in the two circuits be the same?
$(b)$ Can the $rms$ current in circuit $(b)$ be larger than that in $(a)$?