Alternating Current (AC) and Voltage

Interactive Feed

JEE Advanced 2012

In the given circuit, the AC source has $ω = 100 rad/s$ . Considering the inductor and capacitor to be ideal, the correct choice(s) is(are)

I

is approximately

0.3 A

(B)

the current through the circuit,

I

is approximately

0.3 2 A

(C)

the voltage across

100 Ω

resistor =

102 V

(D)

the voltage across

50 Ω

resistor =

10 V

JEE Advanced 2011

LEVELJEE Main

A series $R$ - $C$ circuit is connected to AC voltage source. Consider two cases; ( $A$ ) when $C$ is without a dielectric medium and ( $B$ ) when $C$ is filled with dielectric of constant 4. The current $I_{R}$ through the resistor and voltage $V_{C}$ across the capacitor are compared in the two cases. Which of the following is/are true?

* Multiple Correct Options

(A)

I_{R}^{A} > I_{R}^{B}

(B)

I_{R}^{A} < I_{R}^{B}

(C)

V_{C}^{A} > V_{C}^{B}

(D)

V_{C}^{A} < V_{C}^{B}

LEVELJEE Advanced

An inductor of inductance $2.0 mH$ is connected across a charged capacitor of capacitance $5.0 μ F$ and the resulting $L - C$ circuit is set oscillating at its natural frequency. Let $Q$ denote the instantaneous charge on the capacitor and $I$ , the current in the circuit. It is found that the maximum value of $Q$ is $200 μ C$ . (a) When $Q = 100 μ C$ , what is the value of $\frac{d I}{d t}$ ? (b) When $Q = 200 μ C$ , what is the value of $I$ ? (c) Find the maximum value of $I$ . (d) When $I$ is equal to one-half its maximum value, what is the value of $∣ Q ∣$ ?

JEE Main 2010

LEVELJEE Main

An AC voltage source of variable angular frequency $ω$ and fixed amplitude $V_{0}$ is connected in series with a capacitance $C$ and an electric bulb of resistance $R$ (inductance zero). When $ω$ is increased,

(A)

the bulb glows dimmer

(B)

the bulb glows brighter

(C)

total impedance of the circuit is unchanged

(D)

total impedance of the circuit increases

JEE Advanced 2013

LEVELJEE Main

Comprehension Passage

A thermal power plant produces electric power of

600 kW

4000 V

, which is to be transported to a place

20 km

away from the power plant for consumers' usage. It can be transported either directly with a cable of large current carrying capacity or by using a combination of step-up and step-down transformers at the two ends. The drawback of the direct transmission is the large energy dissipation. In the method of using transformers, the dissipation is much smaller. In this method, a step-up transformer is used at the plant side so that the current is reduced to a smaller value. At the consumers' end, a step-down transformer is used to supply power to the consumers at the specified lower voltage. It is reasonable to assume that the power cable is purely resistive and the transformers are ideal with a power factor unity. All the current and voltages mentioned are rms values.

Question 1:

If the direct transmission method with a cable of resistance $0.4 Ω km^{- 1}$ is used, the power dissipation (in %) during transmission is

(A)

20

(B)

30

(C)

40

(D)

50

Question 2:

In the method using the transformers, assume that the ratio of the number of turns in the primary to that in the secondary in the step-up transformer is $1 : 10$ . If the power to the consumers has to be supplied at $200 V$ , the ratio of the number of turns in the primary to that in the secondary in the step-down transformer is

(A)

200 : 1

(B)

150 : 1

(C)

100 : 1

(D)

50 : 1

JEE Main 2003

LEVELJEE Main

When an AC source of emf $e = E_{0} sin (100 t)$ is connected across a circuit, the phase difference between the emf $e$ and the current $i$ in the circuit is observed to be $\frac{π}{4}$ ahead, as shown in the diagram. If the circuit consists possibly only of $R - C$ or $R - L$ or $L - C$ in series, find the relationship between the two elements.

(A)

R = 1 k Ω, C = 10 μ F

(B)

R = 1 k Ω, C = 1 μ F

(C)

R = 1 k Ω, L = 10 H

(D)

R = 1 k Ω, L = 1 H

JEE Advanced 2011

LEVELJEE Main

A series $R$ - $C$ combination is connected to an AC voltage of angular frequency $ω = 500 rad/s$ . If the impedance of the $R$ - $C$ circuit is $R 1.25$ , the time constant (in millisecond) of the circuit is

JEE Advanced 2004

LEVELJEE Main

In an $L - R$ series circuit, a sinusoidal voltage $V = V_{0} sin ω t$ is applied. It is given that $L = 35 mH$ , $R = 11 Ω$ , $V_{rms} = 220 V$ , $ω /2 π = 50 Hz$ and $π = 22/7$ . Find the amplitude of current in the steady state and obtain the phase difference between the current and the voltage. Also plot the variation of current for one cycle on the given graph.

JEE Advanced 2014

LEVELJEE Advanced

At time $t = 0$ , terminal $A$ in the circuit shown in the figure is connected to $B$ by a key and an alternating current $I (t) = I_{0} cos (ω t)$ , with $I_{0} = 1 A$ and $ω = 500 rad s^{- 1}$ starts flowing in it with the initial direction shown in the figure. At $t = \frac{7 π}{6 ω}$ , the key is switched from $B$ to $D$ . Now onwards only $A$ and $D$ are connected. A total charge $Q$ flows from the battery to charge the capacitor fully. If $C = 20 μ F$ , $R = 10 Ω$ and the battery is ideal with emf of $50 V$ , identify the correct statement(s).

* Multiple Correct Options

(A)

Magnitude of the maximum charge on the capacitor before

t = \frac{7 π}{6 ω}

1 \times 1 0^{- 3} C

(B)

The current in the left part of the circuit just before

t = \frac{7 π}{6 ω}

is clockwise

(C)

Immediately after

A

is connected to

D

, the current in

R

10 A

(D)

Q = 2 \times 1 0^{- 3} C

JEE Advanced 2017

LEVELJEE Advanced

The instantaneous voltages at three terminals marked $X$ , $Y$ and $Z$ are given by $V_{X} = V_{0} sin ω t$ , $V_{Y} = V_{0} sin (ω t + \frac{2 π}{3})$ and $V_{Z} = V_{0} sin (ω t + \frac{4 π}{3})$ . An ideal voltmeter is configured to read rms value of the potential difference between its terminals. It is connected between points $X$ and $Y$ and then between $Y$ and $Z$ . The reading(s) of the voltmeter will be

* Multiple Correct Options

(A)

(V_{Y Z})_{rms} = V_{0} \frac{1}{2}

(B)

(V_{X Y})_{rms} = V_{0} \frac{3}{2}

(C)

independent of the choice of the two terminals

(D)

(V_{X Y})_{rms} = V_{0}

JEE Main 2025

LEVELJEE Advanced

A circuit with an electrical load having impedance $Z$ is connected with an AC source as shown in the diagram. The source voltage varies in time as $V (t) = 300 sin (400 t)$ V, where $t$ is time in s. List-I shows various options for the load. The possible currents $i (t)$ in the circuit as a function of time are given in List-II. Choose the option that describes the correct match between the entries in List-I to those in List-II.

List-I

(P)

R = 30 Ω

(Q)

R = 30 Ω

L = 100 mH

(R)

C = 50 μ F

R = 30 Ω

L = 25 mH

(S)

C = 50 μ F

R = 60 Ω

L = 125 mH

List-II

The circuit shown in the figure contains an inductor L, a capacitor $C_{0}$ , a resistor $R_{0}$ and an ideal battery. The circuit also contains two keys $K_{1}$ and $K_{2}$ . Initially, both the keys are open and there is no charge on the capacitor. At an instant, key $K_{1}$ is closed and immediately after this the current in $R_{0}$ is found to be $I_{1}$ . After a long time, the current attains a steady state value $I_{2}$ . Thereafter, $K_{2}$ is closed and simultaneously $K_{1}$ is opened and the voltage across $C_{0}$ oscillates with amplitude $V_{0}$ and angular frequency $ω_{0}$

\begin{circuitikz}[scale=1.2] \begin{scope}[id=branch_battery] \draw (4,0) to[battery1, l={$20\,\mathrm{V}$}] (0,0); \end{scope} \begin{scope}[id=branch_R] \draw (0,0) to[R, l={$R_0 = 5\,\Omega$}] (0,2); \end{scope} \begin{scope}[id=branch_L] \draw (0,2) to[L, l_={$L = 25\,\mathrm{mH}$}] (4,2); \end{scope} \begin{scope}[id=branch_K1] \draw (4,2) to[nos, l={$K_1$}] (4,0); \end{scope} \begin{scope}[id=branch_top] \draw (0,2) -- (0,3.5) to[nos, l={$K_2$}] (2,3.5) to[C, l={$C_0 = 10\,\mu\mathrm{F}$}] (4,3.5) -- (4,2); \end{scope} \end{circuitikz}

List-I

(P)

The value of

I_{1}

in Ampere is

(Q)

The value of

I_{2}

in Ampere is

(R)

The value of

ω_{0}

in kilo-radians/s

(S)

The value of

V_{0}

in Volt is

List-II

A series LCR circuit is connected to a $45 sin (ω t)$ Volt source. The resonant angular frequency of the circuit is $1 0^{5} rad s^{- 1}$ and current amplitude at resonance is $I_{0}$ . When the angular frequency of the source is $ω = 8 \times 1 0^{4} rad s^{- 1}$ , the current amplitude in the circuit is $0.05 I_{0}$ . If $L = 50 mH$ , match each entry in List-I with an appropriate value from List-II and choose the correct option.

List-I

(P)

I_{0}

in mA

(Q)

The quality factor of the circuit

(R)

The bandwidth of the circuit in

rad s^{- 1}

(S)

The peak power dissipated at resonance in Watt

List-II

Comprehension Passage

In a circuit, a metal filament lamp is connected in series with a capacitor of capacitance

C μ F

across a

200 V

50 Hz

supply. The power consumed by the lamp is

500 W

while the voltage drop across it is

100 V

. Assume that there is no inductive load in the circuit. Take rms values of the voltages. The magnitude of the phase-angle (in degrees) between the current and the supply voltage is

ϕ

. Assume,

π 3 \approx 5

Question 1:

The value of $C$ is _______.

Question 2:

The value of $ϕ$ is _______.

JEE Main 2021

LEVELJEE Advanced

Two circuits are shown in the figures (a) and (b). At a frequency of ......... rad/s, the average power dissipated in one cycle will be same in both the circuits.

JEE Main 2020

LEVELJEE Advanced

In a series $L - R$ circuit, power of $400 W$ is dissipated from a source of $250 V$ , $50 Hz$ . The power factor of the circuit is $0.8$ . In order to bring the power factor to unity, a capacitor of value $C$ is added in series to the $L$ and $R$ . Taking the value of $C$ as $(\frac{n}{3 π}) μ F$ , then value of $n$ is ……… .

JEE Main 2021

LEVELBoard

A resonance circuit having inductance and resistance $2 \times 1 0^{- 4} H$ and $6.28 Ω$ respectively oscillates at $10 MHz$ frequency. The value of quality factor of this resonator is ......... . [Take, $π = 3.14$ ]

LEVELJEE Main

In an oscillating $L - C$ circuit, the maximum charge on the capacitor is $Q$ . The charge on the capacitor when the energy is stored equally between the electric and magnetic fields is

(A)

\frac{Q}{2}

(B)

\frac{Q}{3}

(C)

\frac{Q}{2}

(D)

Q

JEE Main 2019

LEVELJEE Main

A transformer consisting of 300 turns in the primary and 150 turns in the secondary gives output power of 2.2 kW. If the current in the secondary coil is 10 A, then the input voltage and current in the primary coil are

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 of

(A)

4 μ F

(B)

8 μ F

(C)

1 μ F

(D)

2 μ F

JEE Main 2020

LEVELJEE Main

An inductance coil has a reactance of $100 Ω$ . When an AC signal of frequency $1000 Hz$ is applied to the coil, the applied voltage leads the current by $4 5^{\circ}$ . The self-inductance of the coil is

(A)

1.1 \times 1 0^{- 2} H

(B)

1.1 \times 1 0^{- 1} H

(C)

5.5 \times 1 0^{- 5} H

(D)

6.7 \times 1 0^{- 7} H

JEE Main 2021

LEVELJEE Main

A transmitting station releases waves of wavelength $960 m$ . A capacitor of $2.56 μ F$ is used in the resonant circuit. The self-inductance of coil necessary for resonance is ......... $\times 1 0^{- 8} H$ .

LEVELJEE Main

An ideal coil of $10 H$ is connected in series with a resistance of $5 Ω$ and a battery of $5 V$ . After $2 s$ , the connection is made, the current flowing (in ampere) in the circuit is

(A)

1 - e

(B)

e

(C)

e^{- 1}

(D)

1 - e^{- 1}

JEE Main 2021

LEVELJEE Main

An alternating current is given by the equation $i = i_{1} sin ω t + i_{2} cos ω t$ . The rms current will be

(A)

\frac{1}{2} (i_{1}^{2} + i_{2}^{2})^{1/2}

(B)

\frac{1}{2} (i_{1} + i_{2})^{2}

(C)

\frac{1}{2} (i_{1}^{2} + i_{2}^{2})^{1/2}

(D)

\frac{1}{2} (i_{1} + i_{2})

JEE Main 2021

LEVELJEE Main

A series L-C-R circuit of $R = 5Ω$ , $L = 20 mH$ and $C = 0.5 μ F$ is connected across an AC supply of 250 V, having variable frequency. The power dissipated at resonance condition is ...... $\times 1 0^{2} W$ .

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } In the given circuit, the AC source has ω=100 rad/s. Considering the inductor and capacitor to be ideal, the correct choice(s) is(are)

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the direct transmission method with a cable of resistance 0.4Ω km−1 is used, the power dissipation (in %) during transmission is

List-I

List-II

List-I

List-II

List-I

List-II

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The value of C is _______.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The value of ϕ is _______.

Two circuits are shown in the figures (a) and (b). At a frequency of ......... rad/s, the average power dissipated in one cycle will be same in both the circuits.

A transformer consisting of 300 turns in the primary and 150 turns in the secondary gives output power of 2.2 kW. If the current in the secondary coil is 10 A, then the input voltage and current in the primary coil are

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } 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 of

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } An alternating current is given by the equation i=i1​sinωt+i2​cosωt. The rms current will be

In the given circuit, the AC source has $ω = 100 rad/s$ . Considering the inductor and capacitor to be ideal, the correct choice(s) is(are)

If the direct transmission method with a cable of resistance $0.4 Ω km^{- 1}$ is used, the power dissipation (in %) during transmission is

The value of $C$ is _______.

The value of $ϕ$ 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 of

An alternating current is given by the equation $i = i_{1} sin ω t + i_{2} cos ω t$ . The rms current will be