Core Syllabus Module

Current Electricity

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Chapter Elite-20 Challenge Zone

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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.

JEE Advanced 2015

LEVELJEE Advanced

In the following circuit, the current through the resistor $R (= 2Ω)$ is $I$ amperes. The value of $I$ is

JEE Advanced 2022

LEVELJEE Advanced

The figure shows a circuit having eight resistances of $1 Ω$ each, labelled $R_{1}$ to $R_{8}$ , and two ideal batteries with voltages $ε_{1} = 12 V$ and $ε_{2} = 6 V$ . Which of the following statement(s) is(are) correct?

* Multiple Correct Options

(A)

The magnitude of current flowing through

R_{1}

7.2 A

(B)

The magnitude of current flowing through

R_{2}

1.2 A

(C)

The magnitude of current flowing through

R_{3}

4.8 A

(D)

The magnitude of current flowing through

R_{5}

2.4 A

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 Advanced 2004

LEVELJEE Advanced

In the circuit shown $A$ and $B$ are two cells of same emf $E$ but different internal resistances $r_{1}$ and $r_{2}$ ( $r_{1} > r_{2}$ ) respectively. Find the value of $R$ such that the potential difference across the terminals of cell $A$ is zero, a long time after the key $K$ is closed.

LEVELJEE Advanced

A battery of internal resistance $4 Ω$ is connected to the network of resistances as shown in figure. In order that the maximum power can be delivered to the network, the value of $R$ in $Ω$ should be

(A)

\frac{4}{9}

(B)

2

(C)

\frac{8}{3}

(D)

18

JEE Advanced 1981

LEVELJEE Advanced

In the circuit shown in figure $E_{1} = 3 V$ , $E_{2} = 2 V$ , $E_{3} = 1 V$ and $R = r_{1} = r_{2} = r_{3} = 1 Ω$ . (a) Find the potential difference between the points $A$ and $B$ and the currents through each branch. (b) If $r_{2}$ is short-circuited and the point $A$ is connected to point $B$ , find the currents through $E_{1}, E_{2}, E_{3}$ and the resistor $R$ .

LEVELJEE Advanced

In the circuit shown in figure $E$ , $F$ , $G$ and $H$ are cells of emf $2$ , $1$ , $3$ and $1 V$ respectively, and their internal resistances are $2$ , $1$ , $3$ and $1 Ω$ respectively. Calculate (a) the potential difference between $B$ and $D$ and (b) the potential difference across the terminals of each cells $G$ and $H$ .

JEE Advanced 2019

LEVELJEE Advanced

Two identical moving coil galvanometer have $10 Ω$ resistance and full scale deflection at $2 μ A$ current. One of them is converted into a voltmeter of $100 mV$ full scale reading and the other into an Ammeter of $1 mA$ full scale current using appropriate resistors. These are then used to measure the voltage and current in the Ohm's law experiment with $R = 1000 Ω$ resistor by using an ideal cell. Which of the following statement(s) is/are correct ?

* Multiple Correct Options

(A)

The measured value of

R

will be

978 Ω < R < 982 Ω

(B)

The resistance of the Voltmeter will be

100 k Ω

(C)

The resistance of the Ammeter will be

0.02 Ω

(round off to

2^{nd}

decimal place)

(D)

If the ideal cell is replaced by a cell having internal resistance of

5 Ω

then the measured value of

R

will be more than

1000 Ω

JEE Advanced 2022

LEVELJEE Advanced

Two resistances $R_{1} = X Ω$ and $R_{2} = 1 Ω$ are connected to a wire AB of uniform resistivity, as shown in the figure. The radius of the wire varies linearly along its axis from $0.2 mm$ at A to $1 mm$ at B. A galvanometer (G) connected to the center of the wire, $50 cm$ from each end along its axis, shows zero deflection when A and B are connected to a battery. The value of X is _____.

JEE Advanced 2021

LEVELJEE Advanced

In order to measure the internal resistance $r_{1}$ of a cell of emf $E$ , a meter bridge of wire resistance $R_{0} = 50 Ω$ , a resistance $R_{0} /2$ , another cell of emf $E /2$ (internal resistance $r$ ) and a galvanometer $G$ are used in a circuit, as shown in the figure. If the null point is found at $l = 72 cm$ , then the value of $r_{1} =_____Ω$ .

JEE Advanced 2022

LEVELJEE Advanced

In Circuit-1 and Circuit-2 shown in the figures, $R_{1} = 1Ω$ , $R_{2} = 2Ω$ and $R_{3} = 3Ω$ . $P_{1}$ and $P_{2}$ are the power dissipations in Circuit-1 and Circuit-2 when the switches $S_{1}$ and $S_{2}$ are in open conditions, respectively. $Q_{1}$ and $Q_{2}$ are the power dissipations in Circuit-1 and Circuit-2 when the switches $S_{1}$ and $S_{2}$ are in closed conditions, respectively. Which of the following statement(s) is(are) correct?

* Multiple Correct Options

(A)

When a voltage source of 6 V is connected across A and B in both circuits,

P_{1} < P_{2}

(B)

When a constant current source of 2 Amp is connected across A and B in both circuits,

P_{1} > P_{2}

(C)

When a voltage source of 6 V is connected across A and B in Circuit-1,

Q_{1} > P_{1}

(D)

When a constant current source of 2 Amp is connected across A and B in both circuits,

Q_{2} < Q_{1}

JEE Advanced 2020

LEVELJEE Advanced

Shown in the figure is a semicircular metallic strip that has thickness t and resistivity $ρ$ . Its inner radius is $R_{1}$ and outer radius is $R_{2}$ . If a voltage $V_{0}$ is applied between its two ends, a current I flows in it. In addition, it is observed that a transverse voltage $Δ V$ develops between its inner and outer surfaces due to purely kinetic effects of moving electrons (ignore any role of the magnetic field due to the current). Then (figure is schematic and not drawn to scale)-

* Multiple Correct Options

(A)

I = \frac{V _{0} t}{π ρ} ln (\frac{R _{2}}{R _{1}})

(B)

the outer surface is at a higher voltage than the inner surface

(C)

the outer surface is at a lower voltage than the inner surface

(D)

Δ V \propto I^{2}

JEE Main 2020

LEVELJEE Advanced

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 2008

LEVELJEE Advanced

Comprehension Passage

Directions (Q. Nos. 54 to 55) are based on the following paragraph. Consider a block of conducting material of resistivity

ρ

shown in the figure. Current

I

enters at

A

and leaves from

D

. We apply superposition principle to find voltage

Δ V

developed between

B

and

C

. The calculation is done in the following steps (a) Take current

I

entering from

A

and assume it to spread over a hemispherical surface on the block. (b) Calculate field

E (r)

at distance

r

from

A

by using Ohm's law

E = ρ J

, where

J

is the current per unit area at

r

. (c) From the

r

dependence of

E (r)

, obtain the potential

V (r)

r

. (d) Repeat steps (i), (ii) and (iii) for current

I

leaving

D

and superpose results for

A

and

D

Question 1:

$Δ V$ measured between $B$ and $C$ is

(A)

\frac{ρ I}{π a} - \frac{ρ I}{π ( a + b )}

(B)

\frac{ρ I}{a} - \frac{ρ I}{( a + b )}

(C)

\frac{ρ I}{2 π a} - \frac{ρ I}{2 π ( a + b )}

(D)

\frac{ρ I}{2 π ( a - b )}

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 $t = 12 s$ .

Micro-Topic Strategy Matrix

Ohm's Law, Resistance and Electrical Power

Combination of Resistors

Cells, EMF, and Internal Resistance

Kirchhoff's Laws

Electrical Instruments

RC Circuit

Chapter Elite-20 Challenge Zone

.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; } In the following circuit, the current through the resistor R(=2Ω) is I amperes. The value of I is

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } ΔV measured between B and C is

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

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.

In the following circuit, the current through the resistor $R (= 2Ω)$ is $I$ amperes. The value of $I$ is

$Δ V$ measured between $B$ and $C$ is