Pure R, L and C Circuits

The correct phasor diagram for an a.c. circuit containing only pure capacitor.

When a.c. source is connected across a pure capacitor, the correct phase relation between current and emf is shown in figure.

In an a.c. circuit with pure capacitance 'C' and a.c. source $E = E_0 \sin \omega t$, the equation of instantaneous current is given by

Which one of the following graph represents the correct variation of inductive reactance ($X_L$) with angular frequency ($\omega$)?

An inductance of negligible resistance, whose reactance is $120\ \Omega$ at $200$ Hz is connected to a $240$ V, $60$ Hz Power line. The current in the inductor is

A coil has inductive reactance $3$ H. The ratio of its reactance when it is first connected to an a.c. source and then to d.c. source is

An alternating voltage $V = 200\sqrt{2} \sin(100t)$ volt is connected to $1\ \mu F$ capacitor through ammeter (AC). The reading of ammeter is (in mA)

An alternating voltage $V = 200\sqrt{2} \sin(100t)$ volt is connected to $1\ \mu F$ capacitor through a.c. ammeter. The reading of ammeter is

In an a.c. circuit, if the frequency is doubled, what happens to the capacitive reactance ($X_c$) and the current ($I$)?

An alternating voltage $V = 200\sqrt{2} \sin(100t)$ volt is connected to a $1\ \mu$F capacitor through an a.c. ammeter. The reading of the ammeter will be

A capacitor of $10\ \mu F$ has reactance $2 \times 10^{-3}\ \Omega$. The corresponding frequency is

An alternating voltage $e = 150\sqrt{2} \sin 100t$ volt is applied to a capacitor of capacity $2\ \mu$F. The root mean square value of current in the circuit is

In LCR circuit, at a particular angular frequency the capacitive reactance and inductive reactance is same. If the angular frequency is doubled, the ratio of the reactance of the capacitor to that of the inductor will be

Determine the frequency for which a $10\ \mu$F capacitor has a reactance of $2 \times 10^{-3}\ \Omega$.

Same current is flowing in two AC circuits. First contains only inductance and second contains only capacitance. If frequency of AC is increased for both, the current will

An a. c. voltage is applied to pure inductor. The current in the inductor

An a. c. source is connected across a pure inductor. Which one of the following figures shows the correct phase relation between the current and e.m.f.?

In an a.c. circuit with pure capacitance ' C ' and a.c. source $E = E_0 \sin \omega t$, the equation of instantaneous current is given by

A coil has inductance 2 H. The ratio of its reactance when it is connected first to an a.c. source and then to a d.c. source is

The reactance of a capacitor is $X_C$. If the frequency and the capacitance are doubled, then the new reactance will be

Same current is flowing in two different a.c. circuits. First circuit contains only inductance and second contains only capacitance. If the frequency of a.c. is increased in both circuits, the current will

An alternating voltage $E = 100\sqrt{2} \sin(50t)$ is connected to a $2\ \mu F$ capacitor through an a.c. ammeter. The ammeter reading will be

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 capacitor.

Choose the correct answer from the options given below:

A coil has inductance H. The ratio of its reactance when it is connected first to an a.c. source and then to d.c. source is

The inductive reactance of a coil is ' $R$ ' $\Omega$. If inductance of a coil is tripled and frequency of a.c supply is also tripled, then new inductive reactance will be

A 42 mH inductor is connected to $200\text{ V}, 50\text{ Hz}$ a.c. supply. The r.m.s. value of current in the circuit will be nearly [ Take $\pi = \frac{22}{7}$ ]

An alternating voltage $v = 200\sqrt{2} \sin(100t)$ is connected to a $1\ \mu F$ capacitor through an a. c. ammeter. The reading of the ammeter shall be

A $10\ \mu F$ capacitor is connected to a $210\text{ V}, 50\text{ Hz}$ source as shown in figure. The peak current in the circuit is nearly $(\pi = 3.14)$:

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

The magnetic energy in an inductor changes from maximum value to minimum value in 5 ms. When connected to an a.c. source, the frequency of the source is

In the circuit shown below, the inductance $L$ is connected to an ac source. The current flowing in the circuit is $I = I_0 \sin \omega t$. The voltage drop $(V_L)$ across $L$ is

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

In an a.c. circuit the instantaneous current and emf are represented as $I = I_0 \sin[\omega t - \pi/6]$ and $E = E_0 \sin[\omega t + \pi/3]$ respectively. The voltage leads the current by

The inductive reactance of a coil is '$X_L$'. If the inductance of a coil is tripled and frequency of a.c. supply is doubled, then the new inductive reactance will be

An alternating voltage source $V = 260 \sin(628t$) is connected across a pure inductor of $5\text{ mH}$. Inductive reactance in the circuit is:

An alternating voltage $E = 200\sqrt{2} \sin(100t)$ volt is connected to a $1\ \mu F$ capacitor through an a.c. ammeter. The reading of the ammeter shall be

At a particular angular frequency, the reactance of capacitor and that of inductor is same. If the angular frequency is doubled, the ratio of the reactance of the capacitor to that of the inductor will be

The capacitive reactance of a capacitor '$C$' is $X\ \Omega$. Both, the frequency of a.c. supply and capacitance of the above capacitor are doubled. The new capacitive reactance will be

The reactance of capacitor at $50\text{ Hz}$ is $5\ \Omega$. If the frequency is increased to $100\text{ Hz}$, the new reactance is

As per the given graph, choose the correct representation for curve $A$ and curve B. Where $X_C =$ reactance of pure capacitive circuit connected with A.C. source

$X_L =$ reactance of pure inductive circuit connected with A.C. source

R = impedance of pure resistive circuit connected with A.C. source.

$Z =$ Impedance of the LCR series circuit

A capacitor of capacitance $150.0\ \mu F$ is connected to an alternating source of emf given by $E = 36 \sin(120\pi t)\text{ V}$. The maximum value of current in the circuit is approximately equal to:

An ac source is connected to a capacitor C. Due to decrease in its operating frequency

Given below are two statements

Statement I: In an a.c circuit, the current through a capacitor leads the voltage across it. Statement II: In a.c circuit containing pure capacitance only, the phase difference between the current and voltage is $\pi$.

In the light of the above statements, choose the most appropriate answer from the options given below

The resistance offered by an inductor $(X_L)$ in an a.c. circuit is

An inductor of inductance 2 mH is connected to a 220 V, 50 Hz ac source. Let the inductive reactance in the circuit is X1. If a 220 V dc source replace the ac source in the circuit, then the inductive reactance in the circuit is X2. X1 and X2 respectively are:

An alternating emf $E = 440 \sin 100\pi t$ is applied to a circuit containing an inductance of $\frac{\sqrt{2}}{\pi}\text{ H}$. If an a.c. ammeter is connected in the circuit, its reading will be:

A capacitor of capacitance $50\ \mu F$ is connected to a.c. source $e = 220 \sin 50t$ ($e$ in volt, $t$ in second). The value of peak current is

The equation of current in a purely inductive circuit is $5 \sin(49\pi t - 30^\circ)$. If the inductance is $30\text{ mH}$ then the equation for the voltage across the inductor, will be:

$\{$ Let $\pi = \frac{22}{7}\}$

As shown in the figure an inductor of inductance 200 mH is connected to an AC source of emf 220 V and frequency 50 Hz. The instantaneous voltage of the source is 0 V when the peak value of current is $\frac{\sqrt{a}}{\pi}$ A. The value of $a$ is ___________.

In the graphical representation of e.m.f. '$e$' and current '$i$' versus '$\omega t$' for an a.c. circuit, both emf and current reach zero, minimum and maximum value at the same time. The circuit element connected to the source will be

In a circuit consisting of a capacitance and a generator with alternating emf Eg = Eg0 sin$\omega$t, VC and IC are the voltage and current. Correct phasor diagram for such circuit is

Match List - I with List - II

Choose the most appropriate answer from the options given below:

If we increase the frequency of an a.c. supply, then inductive reactance

The inductive reactance of a coil is R$\Omega$. If the inductance of a coil is doubled and frequency of a.c. supply is also doubled then the new inductive reactance will be

What happens to the inductive reactance and the current in a purely inductive circuit if the frequency is halved?

A capacitor of capacitance 'C', is connected across an ac source of voltage V, given by V = V0sin$\omega$t

The displacement current between the plates of the capacitor, would then be given by:

A parallel plate capacitor having plates of radius 6 cm has capacitance 100 pF. It is connected to 230 V a.c. supply with angular frequency 300 rad/s. The r.m.s. value of current is

AC voltage V(t) = 20 sin$\omega$t of frequency 50 Hz is applied to a parallel plate capacitor. The separation between the plates is 2 mm and the area is 1 m2. The amplitude of the oscillating displacement current for the applied AC voltage is _________. [Take $\varepsilon$0 = 8.85 $\times$ 10$-$12 F/m]

A 40 $\mu$F capacitor is connected to a 200 V, 50 Hz ac supply. The rms value of the current in the circuit is, nearly:

A coil has inductance 2 H. The ratio of its reactance, when it is connected first to an $AC$ source and then to DC source, is

A small signal voltage V(t) = V0 sin$\omega$t is applied across an ideal capacitor C

A 100 $\Omega$ resistance and a capacitor of 100 $\Omega$ reactance are connected in series across a 220 V source. When the capacitor is 50% charged, the peak value of the displacement current is

A sinusoidal voltage V(t) = 100 sin (500t) is applied across a pure inductance of L = 0.02 H. The current through the coil is:

In the ac circuit an alternating voltage e = $200\sqrt{2}$sin100t volts is connected to a capacitor of capacity 1 $\mu$F. The r.m.s. value of the current in the circuit is

A capacitor of capacity C has reactance X. If capacitance and frequency become double then reactance will be