RC Circuit

Interactive Feed

JEE Advanced 1988

LEVELJEE Advanced

In the given circuit, $E_{1} = 3 E_{2} = 2 E_{3} = 6 V$ and $R_{1} = 2 R_{4} = 6Ω$ $R_{3} = 2 R_{2} = 4Ω$ , $C = 5 μ F$ . Find the current in $R_{3}$ and the energy stored in the capacitor.

LEVELBoard

A parallel combination of $0.1 M Ω$ resistor and a $10 μ F$ capacitor is connected across a $1.5 V$ source of negligible resistance. The time required for the capacitor to get charged upto $0.75 V$ is approximately (in second)

(A)

infinite

(B)

lo g_{e} 2

(C)

lo g_{10} 2

(D)

zero

LEVELJEE Main

Calculate the steady state current in the $2 Ω$ resistor shown in the circuit (see figure). The internal resistance of the battery is negligible and the capacitance of the condenser $C$ is $0.2 μ F$ .

JEE Main 2006

LEVELJEE Main

Find the time constant for the given RC circuits in correct order (in $μ s$ ). $R_{1} = 1 Ω, R_{2} = 2 Ω, C_{1} = 4 μ F, C_{2} = 2 μ F$ .

At $t = 0$ , switch $S$ is closed. The charge on the capacitor is varying with time as $Q = Q_{0} (1 - e^{- α t})$ . Obtain the value of $Q_{0}$ and $α$ in the given circuit parameters.

LEVELJEE Advanced

A capacitor is charged using an external battery with a resistance $x$ in series. The dashed line shows the variation of $ln I$ with respect to time. If the resistance is changed to $2 x$ , the new graph will be NOTE: Here $I$ is the charging current.

(A)

P

(B)

Q

(C)

R

(D)

S

LEVELJEE Advanced

In the given circuit, with steady current, the potential difference across the capacitor must be

(A)

V

(B)

V /2

(C)

V /3

(D)

2 V /3

JEE Advanced 1986

LEVELJEE Advanced

A part of circuit in a steady state along with the currents flowing in the branches, the values of resistances etc, is shown in the figure. Calculate the energy stored in the capacitor $C$ ( $4 μ F$ ).

JEE Advanced 1997

LEVELJEE Advanced

A leaky parallel plate capacitor is filled completely with a material having dielectric constant $K = 5$ and electrical conductivity $σ = 7.4 \times 1 0^{- 12} Ω^{- 1} m^{- 1}$ . If the charge on the capacitor at instant $t = 0$ is $q = 8.85 μ C$ , then calculate the leakage current at the instant $t = 12 s$ .

JEE Advanced 2010

LEVELJEE Main

At time $t = 0$ , a battery of 10 V is connected across points $A$ and $B$ in the given circuit. If the capacitors have no charge initially, at what time (in second) does the voltage across them become 4 V? [Take : $ln 5 = 1.6$ , $ln 3 = 1.1$ ]

LEVELJEE Main

Capacitor $C_{1}$ of capacitance $1 μ F$ and capacitor $C_{2}$ of capacitance $2 μ F$ are separately charged fully by a common battery. The two capacitors are then separately allowed to discharge through equal resistors at time $t = 0$ .

* Multiple Correct Options

(A)

The currents in each of the two discharging circuits is zero at

t = 0

(B)

The currents in the two discharging circuits at

t = 0

are equal but not zero

(C)

The currents in the two discharging circuits at

t = 0

are unequal

(D)

Capacitor

C_{1}

, loses 50% of its initial charge sooner than

C_{2}

loses 50% of its initial charge

JEE Advanced 2007

LEVELJEE Advanced

A circuit is connected as shown in the figure with the switch $S$ open. When the switch is closed, the total amount of charge that flows from $Y$ to $X$ is

(A)

zero

(B)

54 μ C

(C)

27 μ C

(D)

81 μ C

JEE Advanced 2005

LEVELJEE Main

A $4 μ F$ capacitor and a resistance of $2.5 M Ω$ are in series with $12 V$ battery. Find the time after which the potential difference across the capacitor is 3 times the potential difference across the resistor. [Given, $ln (2) = 0.693$ ]

In the circuit shown below, the key is pressed at time $t = 0$ . Which of the following statement(s) is (are) true?

* Multiple Correct Options

(A)

The voltmeter display

- 5 V

as soon as the key is pressed and displays

+ 5 V

after a long time

(B)

The voltmeter will display

0 V

at time

t = ln 2

seconds

(C)

The current in the ammeter becomes

1/ e

of the initial value after 1 second

(D)

The current in the ammeter becomes zero after a long time

JEE Main 2021

LEVELJEE Advanced

Comprehension Passage

In the circuit shown below, the switch S is connected to position P for a long time so that the charge on the capacitor becomes

q_{1} μ C

. Then S is switched to position Q. After a long time, the charge on the capacitor is

q_{2} μ C

Question 1:

The magnitude of $q_{1}$ is ______ .

Question 2:

The magnitude of $q_{2}$ is ______ .

JEE Advanced 2023

LEVELJEE Advanced

In a circuit shown in the figure, the capacitor C is initially uncharged and the key K is open. In this condition, a current of 1 A flows through the $1Ω$ resistor. The key is closed at time $t = t_{0}$ . Which of the following statement(s) is(are) correct? [Given: $e^{- 1} = 0.36$ ]

* Multiple Correct Options

(A)

The value of the resistance R is

3Ω

(B)

For

t < t_{0}

, the value of current

I_{1}

is 2A.

(C)

t = t_{0} + 7.2 μ s

, the current in the capacitor is 0.6 A.

(D)

For

t \to \infty

, the charge on the capacitor is

12 μ C

JEE Advanced 2019

LEVELJEE Advanced

In the circuit shown, initially there is no charge on capacitors and keys $S_{1}$ and $S_{2}$ are open. The values of the capacitors are $C_{1} = 10 μ F$ , $C_{2} = 30 μ F$ and $C_{3} = C_{4} = 80 μ F$ . Which of the statement(s) is/are correct ?

* Multiple Correct Options

(A)

The keys

S_{1}

is kept closed for long time such that capacitors are fully charged. Now key

S_{2}

is closed, at this time, the instantaneous current across

30 Ω

resistor (between points P and Q) will be

0.2 A

(round off to

1^{st}

decimal place).

(B)

If key

S_{1}

is kept closed for long time such that capacitors are fully charged, the voltage difference between points P and Q will be

10 V

(C)

At time

t = 0

, the key

S_{1}

is closed, the instantaneous current in the closed circuit will be

25 mA

(D)

If key

S_{1}

is kept closed for long time such that capacitors are fully charged, the voltage across the capacitors

C_{1}

will be

4 V

JEE Main 2017

LEVELJEE Main

In the given circuit diagram, when the current reaches steady state in the circuit, the charge on the capacitor of capacitance $C$ will be

(A)

C E \frac{r _{1}}{( r _{2} + r )}

(B)

C E \frac{r _{2}}{( r + r _{2} )}

(C)

C E \frac{r _{1}}{( r _{1} + r )}

(D)

C E

JEE Main 2013

LEVELJEE Main

In an $L - C - R$ circuit as shown below, both switches are open initially. Now, switch $S_{1}$ is closed and $S_{2}$ kept open ( $q$ is charge on the capacitor and $τ = R C$ is capacitance time constant). Which of the following statement is correct?

(A)

Work done by the battery is half of the energy dissipated in the resistor

(B)

t = τ, q = C V /2

(C)

t = 2 τ, q = C V (1 - e^{- 2})

(D)

t = \frac{τ}{2}, q = C V (1 - e^{- 1})

JEE Main 2011

LEVELJEE Advanced

A resistor $R$ and $2 μ F$ capacitor in series is connected through a switch to $200 V$ direct supply. Across the capacitor is a neon bulb that lights up at $120 V$ . Calculate the value of $R$ to make the bulb light up $5 s$ after the switch has been closed (take $lo g_{10} 2.5 = 0.4$ )

(A)

1.7 \times 1 0^{5} Ω

(B)

2.7 \times 1 0^{6} Ω

(C)

3.3 \times 1 0^{7} Ω

(D)

1.3 \times 1 0^{4} Ω

JEE Main 2020

LEVELJEE Advanced

For the given input voltage waveform $V_{in} (t)$ , the output voltage waveform $V_{o u t} (t)$ , across the capacitor is correctly depicted by

An ideal cell of emf 10 V is connected in circuit shown in figure. Each resistance is $2 Ω$ . The potential difference (in V) across the capacitor when it is fully charged is ......... .

JEE Main 2019

LEVELJEE Main

Determine the charge on the capacitor in the following circuit

(A)

2 μ C

(B)

200 μ C

(C)

10 μ C

(D)

60 μ C

JEE Main 2021

LEVELJEE Main

The circuit shown in the figure consists of a charged capacitor of capacity $3 μ F$ and a charge of $30 μ C$ . At time $t = 0$ , when the key is closed, the value of current flowing through the $5 M Ω$ resistor is $xμ A$ . The value of $x$ to the nearest integer is ......... .

JEE Main 2021

LEVELJEE Main

An $R - C$ circuit as shown in the figure is driven by an AC source generating a square wave. The output wave pattern monitored by CRO would look close to

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } In the given circuit, E1​=3E2​=2E3​=6 V and R1​=2R4​=6Ω R3​=2R2​=4Ω, C=5μF. Find the current in R3​ and the energy stored in the capacitor.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Find the time constant for the given RC circuits in correct order (in μs). R1​=1Ω,R2​=2Ω,C1​=4μF,C2​=2μF.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } At t=0, switch S is closed. The charge on the capacitor is varying with time as Q=Q0​(1−e−αt). Obtain the value of Q0​ and α in the given circuit parameters.

In the given circuit, with steady current, the potential difference across the capacitor must be

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A circuit is connected as shown in the figure with the switch S open. When the switch is closed, the total amount of charge that flows from Y to X is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } In the circuit shown below, the key is pressed at time t=0. Which of the following statement(s) is (are) true?

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The magnitude of q1​ is ______ .

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The magnitude of q2​ is ______ .

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } In the given circuit diagram, when the current reaches steady state in the circuit, the charge on the capacitor of capacitance C will be

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } For the given input voltage waveform Vin​(t), the output voltage waveform Vout​(t), across the capacitor is correctly depicted by

Determine the charge on the capacitor in the following circuit

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } An R−C circuit as shown in the figure is driven by an AC source generating a square wave. The output wave pattern monitored by CRO would look close to

In the given circuit, $E_{1} = 3 E_{2} = 2 E_{3} = 6 V$ and $R_{1} = 2 R_{4} = 6Ω$ $R_{3} = 2 R_{2} = 4Ω$ , $C = 5 μ F$ . Find the current in $R_{3}$ and the energy stored in the capacitor.

Find the time constant for the given RC circuits in correct order (in $μ s$ ). $R_{1} = 1 Ω, R_{2} = 2 Ω, C_{1} = 4 μ F, C_{2} = 2 μ F$ .

At $t = 0$ , switch $S$ is closed. The charge on the capacitor is varying with time as $Q = Q_{0} (1 - e^{- α t})$ . Obtain the value of $Q_{0}$ and $α$ in the given circuit parameters.

A circuit is connected as shown in the figure with the switch $S$ open. When the switch is closed, the total amount of charge that flows from $Y$ to $X$ is

In the circuit shown below, the key is pressed at time $t = 0$ . Which of the following statement(s) is (are) true?

The magnitude of $q_{1}$ is ______ .

The magnitude of $q_{2}$ is ______ .

In the given circuit diagram, when the current reaches steady state in the circuit, the charge on the capacitor of capacitance $C$ will be

For the given input voltage waveform $V_{in} (t)$ , the output voltage waveform $V_{o u t} (t)$ , across the capacitor is correctly depicted by

An $R - C$ circuit as shown in the figure is driven by an AC source generating a square wave. The output wave pattern monitored by CRO would look close to