Alternating Current

A LCR series circuit driven with $E_{r m s}=90 \mathrm{~V}$ at frequency $f_{\mathrm{d}}=30 \mathrm{~Hz}$ has resistance $R=80 \Omega$, an inductance with inductive reactance $X_L=20.0 \Omega$ and capacitance with capacitive reactance $X_C=...

An a.c. source of angular frequency $\omega$ is connected across a resistor $R$ and a capacitor $C$ in series. The current is observed as $I$. Now the frequency of the source is changed to $\omega / 4$, (keeping the voltage unchanged) the c...

A series LCR circuit with $R=20 \Omega, L=1.6 \mathrm{H}$ and $C=40 \mu \mathrm{~F}$ is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is $\_\_\_\_$ $\Omega$.

An inductor of 10 mH , capacitor of $0.1 \mu \mathrm{~F}$ and a resistor of $100 \Omega$ are connected in series across an $a . c$ power supply $220 \mathrm{~V}, 70 \mathrm{~Hz}$. The power factor of the given circuit is 0.5 . The differenc...

The figure given below shows an LCR series circuit with two switches S1 and S2. When switch S1 is closed keeping S2 open, the phase difference (φ) between the current and source voltage is 30° and phase difference is 60° when S2 is closed k...

The electric current in the circuit is given as $i=i_{\mathrm{o}}(t / T)$. The r.m.s current for the period $t=0$ to $t=T$ is $\_\_\_\_$ .

An inductor stores 16 J of magnetic field energy and dissipates 32 W of thermal energy due to its resistance when an a.c. current of 2 A (rms) and frequency 50 Hz flows through it. The ratio of inductive reactance to its resistance is _____...

For the series LCR circuit connected with $220 \mathrm{~V}, 50 \mathrm{~Hz}$ a.c source as shown in the figure, the power factor is $\frac{\alpha}{10}$. The value of $\alpha$ is $\_\_\_\_$ .

Using a variable frequency a.c. voltage source the maximum current measured in the given LCR circuit is 50 mA for $V=5 \sin (100 t)$ The values of $L$ and $R$ are shown in the figure. The capacitance of the capacitor ( C ) used is $\_\_\_\_...

A capacitor C is first charged fully with potential difference of $V_0$ and disconnected from the battery. The charged capacitor is connected across an inductor having inductance L. In $t$ s, 25% of the initial energy in the capacitor is tr...

For ac circuit shown in figure, $\mathrm{R}=100 \mathrm{k} \Omega$ and $\mathrm{C}=100 \mathrm{pF}$ and the phase difference between $\mathrm{V}_{\text {in }}$ and $\left(\mathrm{V}_{\mathrm{B}}-\mathrm{V}_{\mathrm{A}}\right)$ is $90^{\circ...

An ac current is represented as
\(i=5 \sqrt{2}+10 \cos \left(650 \pi t+\frac{\pi}{6}\right) A m p\)
The r.m.s value of the current is

An inductor of reactance $100 \Omega$, a capacitor of reactance $50 \Omega$, and a resistor of resistance $50 \Omega$ are connected in series with an AC source of $10 \mathrm{~V}, 50 \mathrm{~Hz}$. Average power dissipated by the circuit is...

An alternating current is represented by the equation,
$i=100 \sqrt{2} \sin (100 \pi t)$ ampere. The RMS value of current and the frequency of the given alternating current are

An inductor of self inductance 1 H is connected in series with a resistor of $100 \pi$ ohm and an ac supply of $100 \pi$ volt, 50 Hz . Maximum current flowing in the circuit is _________ A.

An electric bulb rated as $100 \mathrm{~W}-220 \mathrm{~V}$ is connected to an ac source of rms voltage 220 V. The peak value of current through the bulb is :

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent m...

In the circuit shown here, assuming threshold voltage of diode is negligibly small, then voltage $ V_{AB} $ is correctly represented by:

An alternating current is given by $\mathrm{I}=\mathrm{I}_{\mathrm{A}} \sin \omega \mathrm{t}+\mathrm{I}_{\mathrm{B}} \cos \omega \mathrm{t}$. The r.m.s current will be

In a series LCR circuit, a resistor of $300 \Omega$, a capacitor of 25 nF and an inductor of 100 mH are used. For maximum current in the circuit, the angular frequency of the ac source is _________ $\times 10^4$ radians $\mathrm{s}^{-1}$

A series LCR circuit is connected to an alternating source of emf E. The current amplitude at resonant frequency is $I_0$. If the value of resistance R becomes twice of its initial value then amplitude of current at resonance will be

When a coil is connected across a \(20 \mathrm{~V}\) dc supply, it draws a current of \(5 \mathrm{~A}\). When it is connected across \(20 \mathrm{~V}, 50 \mathrm{~Hz}\) ac supply, it draws a current of \(4 \mathrm{~A}\). The self inductance...

A bulb and a capacitor are connected in series across an ac supply. A dielectric is then placed between the plates of the capacitor. The glow of the bulb :

A capacitor of reactance \(4 \sqrt{3} \Omega\) and a resistor of resistance \(4 \Omega\) are connected in series with an ac source of peak value \(8 \sqrt{2} \mathrm{~V}\). The power dissipation in the circuit is __________ W.

A LCR circuit is at resonance for a capacitor C, inductance L and resistance R. Now the value of resistance is halved keeping all other parameters same. The current amplitude at resonance will be now:

An alternating emf \(\mathrm{E}=110 \sqrt{2} \sin 100 \mathrm{t}\) volt is applied to a capacitor of \(2 \mu \mathrm{F}\), the rms value of current in the circuit is ________ \(\mathrm{mA}\).

A coil of negligible resistance is connected in series with \(90 \Omega\) resistor across \(120 \mathrm{~V}, 60 \mathrm{~Hz}\) supply. A voltmeter reads \(36 \mathrm{~V}\) across resistance. Inductance of the coil is :

When a \(d c\) voltage of \(100 \mathrm{~V}\) is applied to an inductor, a \(d c\) current of \(5 \mathrm{~A}\) flows through it. When an ac voltage of \(200 \mathrm{~V}\) peak value is connected to inductor, its inductive reactance is foun...

Given below are two statements :
Statement I : In an LCR series circuit, current is maximum at resonance.
Statement II : Current in a purely resistive circuit can never be less than that in a series LCR circuit when connected to same voltag...

For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is \(2.5 \mathrm{~nF}\). If resistance of \(200 \Omega\) and \(100 \mathrm{~mH}\) inductor is being used in the given circuit. The f...

An ac source is connected in given series LCR circuit. The rms potential difference across the capacitor of \(20 \mu \mathrm{F}\) is __________ V.

An alternating voltage of amplitude \(40 \mathrm{~V}\) and frequency \(4 \mathrm{~kHz}\) is applied directly across the capacitor of \(12 \mu \mathrm{F}\). The maximum displacement current between the plates of the capacitor is nearly :

A series LCR circuit is subjected to an ac signal of \(200 \mathrm{~V}, 50 \mathrm{~Hz}\). If the voltage across the inductor \((\mathrm{L}=10 \mathrm{~mH})\) is \(31.4 \mathrm{~V}\), then the current in this circuit is _______.

A alternating current at any instant is given by \(i=[6+\sqrt{56} \sin (100 \pi t+\pi / 3)]\) A. The \(r m s\) value of the current is ______ A.

In an ac circuit, the instantaneous current is zero, when the instantaneous voltage is maximum. In this case, the source may be connected to :
A. pure inductor.
B. pure capacitor.
C. pure resistor.
D. combination of an inductor and capacito...

Match List I with List II

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An AC voltage \(V=20 \sin 200 \pi t\) is applied to a series LCR circuit which drives a current \(I=10 \sin \left(200 \pi t+\frac{\pi}{3}\right)\). The average power dissipated is:

A series L.R circuit connected with an ac source \(E=(25 \sin 1000 t) V\) has a power factor of \(\frac{1}{\sqrt{2}}\). If the source of emf is changed to \(\mathrm{E}=(20 \sin 2000 \mathrm{t}) \mathrm{V}\), the new power factor of the circ...

Primary coil of a transformer is connected to \(220 \mathrm{~V}\) ac. Primary and secondary turns of the transforms are 100 and 10 respectively. Secondary coil of transformer is connected to two series resistances shown in figure. The outpu...

A power transmission line feeds input power at \(2.3 \mathrm{~kV}\) to a step down transformer with its primary winding having 3000 turns. The output power is delivered at \(230 \mathrm{~V}\) by the transformer. The current in the primary o...

An alternating voltage \(V(t)=220 \sin 100 \pi t\) volt is applied to a purely resistive load of \(50 \Omega\). The time taken for the current to rise from half of the peak value to the peak value is:

A capacitor of capacitance \(100 \mu \mathrm{F}\) is charged to a potential of \(12 \mathrm{~V}\) and connected to a \(6.4 \mathrm{~mH}\) inductor to produce oscillations. The maximum current in the circuit would be :

In an a.c. circuit, voltage and current are given by:
\(V=100 \sin (100 t) V\) and
\(I=100 \sin \left(100 t+\frac{\pi}{3}\right) \mathrm{mA}\) respectively.
The average power dissipated in one cycle is:

A series LCR circuit with \(\mathrm{L}=\frac{100}{\pi} \mathrm{mH}, \mathrm{C}=\frac{10^{-3}}{\pi} \mathrm{F}\) and \(\mathrm{R}=10 \Omega\), is connected across an ac source of \(220 \mathrm{~V}, 50 \mathrm{~Hz}\) supply. The power factor ...

Primary side of a transformer is connected to \(230 \mathrm{~V}, 50 \mathrm{~Hz}\) supply. Turns ratio of primary to secondary winding is \(10: 1\). Load resistance connected to secondary side is \(46 \Omega\). The power consumed in it is :

In series LCR circuit, the capacitance is changed from $C$ to $4 C$. To keep the resonance frequency unchanged, the new inductance should be:

A parallel plate capacitor has a capacitance $\mathrm{C}=200~ \mathrm{pF}$. It is connected to $230 \mathrm{~V}$ ac supply with an angular frequency $300~ \mathrm{rad} / \mathrm{s}$. The rms value of conduction current in the circuit and di...

An oscillating LC circuit consists of a \(75 ~\mathrm{mH}\) inductor and a \(1.2 ~\mu \mathrm{F}\) capacitor. If the maximum charge to the capacitor is \(2.7 ~\mu \mathrm{C}\). The maximum current in the circuit will be ___________ $$\mathr...

A series combination of resistor of resistance \(100 ~\Omega\), inductor of inductance \(1 ~\mathrm{H}\) and capacitor of capacitance \(6.25 ~\mu \mathrm{F}\) is connected to an ac source. The quality factor of the circuit will be _________...

An ideal transformer with purely resistive load operates at \(12 ~\mathrm{kV}\) on the primary side. It supplies electrical energy to a number of nearby houses at \(120 \mathrm{~V}\). The average rate of energy consumption in the houses ser...