Ohm's Law, Resistance and Electrical Power

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JEE Main 2021, 24 Feb Shift-II

A cylindrical wire of radius $0.5 mm$ and conductivity $5 \times 1 0^{7} S/m$ is subjected to an electric field of $10 mV/m$ . The expected value of current in the wire will be $x^{3} π mA$ . The value of $x$ is ......... .

The potential difference applied to an X-ray tube is $5 kV$ and the current through it is $3.2 mA$ . Then the number of electrons striking the target per second is

2 \times 1 0^{16}

(B)

5 \times 1 0^{6}

(C)

1 \times 1 0^{17}

(D)

4 \times 1 0^{15}

JEE Advanced 2016

LEVELJEE Advanced

An infinite line charge of uniform electric charge density $λ$ lies along the axis of an electrically conducting infinite cylindrical shell of radius $R$ . At time $t = 0$ , the space inside the cylinder is filled with a material of permittivity $ε$ and electrical conductivity $σ$ . The electrical conduction in the material follows Ohm's law. Which one of the following graphs best describes the subsequent variation of the magnitude of current density $j (t)$ at any point in the material?

Column I gives certain situations in which a straight metallic wire of resistance $R$ is used and Column II gives some resulting effects. Match the statements in Column I with the statements in Column II.

List-I

(P)

A charged capacitor is connected to the ends of the wire

(Q)

The wire is moved perpendicular to its length with a constant velocity in a uniform magnetic field perpendicular to the plane of motion

(R)

The wire is placed in a constant electric field that has a direction along the length of the wire

(S)

A battery of constant emf is connected to the ends of the wire

List-II

(1)

A constant current flows through the wire

(2)

Thermal energy is generated in the wire

(3)

A constant potential difference develops between the ends of the wire

(4)

Charges of same magnitude appear at the ends of the wire

LEVELJEE Main

Read the following statements carefully $Y$ : The resistivity of semiconductor decreases with increase of temperature. $Z$ : In a conducting solid, the rate of collisions between free electrons and ions increase with increase of temperature. Select the correct statement (s) from the following

(A)

Y

is true but

Z

is false

(B)

Y

is false but

Z

is true

(C)

Both

Y

and

Z

are true

(D)

Y

is true and

Z

is the correct reason for

Y

LEVELJEE Main

A wire of length $L$ and 3 identical cells of negligible internal resistances are connected in series. Due to the current, the temperature of the wire is raised by $Δ T$ in a time $t$ . A number $N$ of similar cells is now connected in series with a wire of the same material and cross-section but of length $2 L$ . The temperature of the wire is raised by the same amount $Δ T$ in the same time. The value of $N$ is

A $25 W$ and a $100 W$ bulb are joined in series and connected to the mains. Which bulb will glow brighter ?

JEE Advanced 1978

LEVELJEE Main

A copper wire is stretched to make it $0.1%$ longer. What is the percentage change in its resistance ?

JEE Advanced 2016

LEVELJEE Advanced

An incandescent bulb has a thin filament of tungsten that is heated to high temperature by passing an electric current. The hot filament emits black-body radiation. The filament is observed to break up at random locations after a sufficiently long time of operation due to non-uniform evaporation of tungsten from the filament. If the bulb is powered at constant voltage, which of the following statement(s) is (are) true?

* Multiple Correct Options

(A)

The temperature distribution over the filament is uniform.

(B)

The resistance over small sections of the filament decreases with time.

(C)

The filament emits more light at higher band of frequencies before it breaks up.

(D)

The filament consumes less electrical power towards the end of the life of the bulb.

LEVELJEE Main

Consider a thin square sheet of side $L$ and thickness $t$ , made of a material of resistivity $ρ$ . The resistance between two opposite faces, shown by the shaded areas in the figure is

(A)

directly proportional to

L

(B)

directly proportional to

t

(C)

independent of

L

(D)

independent of

t

LEVELJEE Main

A piece of copper and another of germanium are cooled from room temperature to $80 K$ . The resistance of

(A)

each of them increases

(B)

each of them decreases

(C)

copper increases and germanium decreases

(D)

copper decreases and germanium increases

LEVELJEE Main

Two bars of radius $r$ and $2 r$ are kept in contact as shown. An electric current $I$ is passed through the bars. Which one of following is correct ?

(A)

Heat produced in bar

B C

is 4 times the heat produced in bar

A B

(B)

Electric field in both halves is equal

(C)

Current density across

A B

is double that of across

B C

(D)

Potential difference across

A B

is 4 times that of across

B C

LEVELJEE Main

In the circuit shown in figure the heat produced in the $5Ω$ resistor due to the current flowing through it is $10 cal/s$ . The heat generated in the $4Ω$ resistor is

A heater is designed to operate with a power of $1000 W$ in a $100 V$ line. It is connected in combination with a resistance of $10 Ω$ and a resistance $R$ , to a $100 V$ mains as shown in the figure. What will be the value of $R$ so that the heater operates with a power of $62.5 W$ ?

LEVELJEE Main

Three resistances of equal value are arranged in the different combinations shown below. Arrange them in increasing order of power dissipation

In an aluminium (Al) bar of square cross section, a square hole is drilled and is filled with iron (Fe) as shown in the figure. The electrical resistivities of Al and Fe are $2.7 \times 1 0^{- 8} Ω m$ and $1.0 \times 1 0^{- 7} Ω m$ , respectively. The electrical resistance between the two faces P and Q of the composite bar is

(A)

\frac{2475}{64} μ Ω

(B)

\frac{1875}{64} μ Ω

(C)

\frac{1875}{49} μ Ω

(D)

\frac{2475}{132} μ Ω

JEE Main 2010

LEVELJEE Main

Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with the increase in temperature. If at room temperature, $100 W$ , $60 W$ and $40 W$ bulbs have filament resistances $R_{100}$ , $R_{60}$ and $R_{40}$ , respectively, the relation between these resistances is

(A)

\frac{1}{R _{100}} = \frac{1}{R _{40}} + \frac{1}{R _{60}}

(B)

R_{100} = R_{40} + R_{60}

(C)

R_{100} > R_{60} > R_{40}

(D)

\frac{1}{R _{100}} > \frac{1}{R _{60}} > \frac{1}{R _{40}}

JEE Main 1987

LEVELBoard

An electric bulb rated for 500 W at 100 V is used in a circuit having a 200 V supply. The resistance $R$ that must be put in series with the bulb, so that the bulb delivers 500 W is ...... $Ω$ .

JEE Advanced 1997

LEVELJEE Main

A steady current flows in a metallic conductor of non-uniform cross-section. The quantity/quantities constant along the length of the conductor is/are

(A)

current, electric field and drift speed

(B)

drift speed only

(C)

current and drift speed

(D)

current only

LEVELJEE Main

A 100 W bulb $B_{1}$ , and two 60 W bulbs $B_{2}$ and $B_{3}$ , are connected to a 250 V source, as shown in the figure. Now $W_{1}, W_{2}$ and $W_{3}$ are the output powers of the bulbs $B_{1}, B_{2}$ and $B_{3}$ respectively. Then,

(A)

W_{1} > W_{2} = W_{3}

(B)

W_{1} > W_{2} > W_{3}

(C)

W_{1} < W_{2} = W_{3}

(D)

W_{1} < W_{2} < W_{3}

JEE Advanced 2026

LEVELJEE Advanced

A metal wire of cross-sectional area $0.5 mm^{2}$ and length $100 m$ is connected across a battery of e.m.f. $2 V$ and internal resistance $1 Ω$ . The density, atomic mass and electrical conductivity of the metal are $6.35 \times 1 0^{3} kg m^{- 3}$ , $63.5 gm/mole$ and $2 \times 1 0^{8} mho m^{- 1}$ , respectively. Assuming one conduction electron per atom of the metal, the drift velocity (in $mm s^{- 1}$ ) of the electrons in the wire is: [Take Avogadro's number as $6 \times 1 0^{23}$ and charge of the electron as $1.6 \times 1 0^{- 19} C$ .]

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}

LEVELJEE Advanced

Two conductors have the same resistance at $0^{\circ} C$ but their temperature coefficients of resistance are $α_{1}$ and $α_{2}$ . The respective temperature coefficients of their series and parallel combinations are nearly

(A)

\frac{α _{1} + α _{2}}{2}, α_{1} + α_{2}

(B)

α_{1} + α_{2}, \frac{α _{1} + α _{2}}{2}

(C)

α_{1} + α_{2}, \frac{α _{1} α _{2}}{α _{1} + α _{2}}

(D)

\frac{α _{1} + α _{2}}{2}, \frac{α _{1} + α _{2}}{2}

LEVELJEE Main

If $400Ω$ of resistance is made by adding four $100Ω$ resistance of tolerance 5%, then the tolerance of the combination is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The potential difference applied to an X-ray tube is 5 kV and the current through it is 3.2 mA. Then the number of electrons striking the target per second is

List-I

List-II

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A 25 W and a 100 W bulb are joined in series and connected to the mains. Which bulb will glow brighter ?

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A copper wire is stretched to make it 0.1% longer. What is the percentage change in its resistance ?

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A piece of copper and another of germanium are cooled from room temperature to 80 K. The resistance of

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Two bars of radius r and 2r are kept in contact as shown. An electric current I is passed through the bars. Which one of following is correct ?

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } In the circuit shown in figure the heat produced in the 5Ω resistor due to the current flowing through it is 10 cal/s. The heat generated in the 4Ω resistor is

Three resistances of equal value are arranged in the different combinations shown below. Arrange them in increasing order of power dissipation

A steady current flows in a metallic conductor of non-uniform cross-section. The quantity/quantities constant along the length of the conductor is/are

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If 400Ω of resistance is made by adding four 100Ω resistance of tolerance 5%, then the tolerance of the combination is

The potential difference applied to an X-ray tube is $5 kV$ and the current through it is $3.2 mA$ . Then the number of electrons striking the target per second is

A $25 W$ and a $100 W$ bulb are joined in series and connected to the mains. Which bulb will glow brighter ?

A copper wire is stretched to make it $0.1%$ longer. What is the percentage change in its resistance ?

A piece of copper and another of germanium are cooled from room temperature to $80 K$ . The resistance of

Two bars of radius $r$ and $2 r$ are kept in contact as shown. An electric current $I$ is passed through the bars. Which one of following is correct ?

In the circuit shown in figure the heat produced in the $5Ω$ resistor due to the current flowing through it is $10 cal/s$ . The heat generated in the $4Ω$ resistor is

If $400Ω$ of resistance is made by adding four $100Ω$ resistance of tolerance 5%, then the tolerance of the combination is