Current Electricity

A wire of resistance \(9\text{ }\Omega\) is bent into the shape of an equilateral triangle. What is the equivalent resistance between any two vertices of the triangle?

(Shift I Memory Based)

A wire of resistance \(9\text{ }\Omega\) is bent into the shape of an equilateral triangle. What is the equivalent resistance between any two vertices of the triangle?

(Shift I Memory Based)

Wheatstone bridge principle is used to measure the specific resistance \(\left(S_1\right)\) of given wire, having length \(L\), radius \(r\). If \(X\) is the resistance of wire, then specific resistance is ; \(S_1=X\left(\frac{\pi r^2}{L}\right)\). If the length of the wire gets doubled then the value of specific resistance will be :

[JEE Main 2024, 27 Jan (Shift 2)]

Wheatstone bridge principle is used to measure the specific resistance \(\left(S_1\right)\) of given wire, having length \(L\), radius \(r\). If \(X\) is the resistance of wire, then specific resistance is ; \(S_1=X\left(\frac{\pi r^2}{L}\right)\). If the length of the wire gets doubled then the value of specific resistance will be :

[JEE Main 2024, 27 Jan (Shift 2)]

Statement I: When non-ideal batteries are connected in parallel, the resultant EMF is less than either of the batteries.

Statement II: When non-ideal batteries are connected in parallel, the resultant resistance of their internal resistances is smaller than either of the individual resistances.

Choose the correct option which is given below:(JEE Mains - 21 Jan 2025 - Shift I Memory Based)

In a metre-bridge when a resistance in the left gap is \(2 \Omega\) and unknown resistance in the right gap, the balance length is found to be \(40 cm\). On shunting the unknown resistance with \(2 \Omega\), the balance length changes by:

StartFragment [1-Feb.-2024_JEE Main (Shift-II)]EndFragment

Given below are two statements :
Statement-I: The equivalent emf of two non-ideal batteries connected in parallel is smaller than either of the two emfs.
Statement-II : The equivalent internal resistance of two non-ideal batteries connected in parallel is smaller than the internal resistance of either of the two batteries.
In the light of the above statements, choose the correct answer from the options given below.

Wheatstone bridge principle is used to measure the specific resistance \(\left(S_1\right)\) of given wire, having length \(L\), radius \(r\). If \(X\) is the resistance of wire, then specific resistance is ; \(S_1=X\left(\frac{\pi r^2}{L}\right)\). If the length of the wire gets doubled then the value of specific resistance will be :

A motor operating on 100 V draws a current of 1 A. If the efficiency of the motor is 91.6%, then the loss of power in units of cal/s is

[JEE Main 2025, 3 Apr (Shift 2)]

Given below are two statements :
Statement-I: The equivalent emf of two nonideal batteries connected in parallel is smaller than either of the two emis.
Statement-II : The equivalent internal resistance of two nonideal batteries connected in parallel is smaller than the internal resistance of either of the two batteries.
In the light of the above statements, choose the correct answer from the options given below.

[JEE Main 2025, 22 Jan (Shift 1)]

Current passing through a wire as function of time is given as I(t) = 0.02t + 0.01 A. The charge that will flow through the wire from t = 1s to t = 2s is :

[JEE Main 2025, 4 Apr (Shift 1)]

The electric current through a wire varies with time as \(\mathrm{I}=\mathrm{I}_{0}+\beta \mathrm{t}\), where \(\mathrm{I}_{0}=20 \mathrm{~A}\) and \(\beta=3 \mathrm{~A} / \mathrm{s}\). The amount of electric charge crossed through a section of the wire in \(20 \mathrm{~s}\) is :

[JEE Main 2024, 29 Jan (Shift 1)]

The electric current through a wire varies with time as \(\mathrm{I}=\mathrm{I}_{0}+\beta \mathrm{t}\), where \(\mathrm{I}_{0}=20 \mathrm{~A}\) and \(\beta=3 \mathrm{~A} / \mathrm{s}\). The amount of electric charge crossed through a section of the wire in \(20 \mathrm{~s}\) is :

[JEE Main 2024, 29 Jan (Shift 1)]

Two resistors of \(200\Omega\) and \(400\Omega\) are connected in series with a battery of 100 V . A bulb rated at 200 V, 100 W is connected across the \(400\Omega\) resistance. The potential drop across the bulb is _________ V.

[02 April, 2026 (Shift-2)]

Statement I: When non-ideal batteries are connected in parallel, the resultant EMF is less than either of the batteries.

Statement II: When non-ideal batteries are connected in parallel, the resultant resistance of their internal resistances is smaller than either of the individual resistances.

Choose the correct option which is given below:(JEE Mains - 21 Jan 2025 - Shift I Memory Based)

A galvanometer having a coil of resistance \(30\Omega\) need 20 mA of current for full-scale deflection. If a maximum current of 3 A is to be measured using this galvanometer, the resistance of the shunt to be added to the galvanometer should be \(\frac{30}{X}\Omega\), where\(X\) is

[JEE Main 2025, 23 Jan (Shift 2)]

Two conductors have the same resistances at \(0^{\circ} \mathrm{C}\) but their temperature coefficients of resistance are \({\alpha }_{1}\)and \({\alpha }_{2}\). The respective temperature coefficients for their series and parallel combinations are :

A wire of resistance \(R\) and length \(L\) is cut into 5 equal parts. If these parts are joined parallely, then resultant resistance will be :

There are ‘n’ number of identical electric bulbs, each is designed to draw a power p independently from the mains supply. They are now joined in series across the main supply. The total power drawn by the combination is :

[JEE Main 2025, 4 Apr (Shift 2)]

A wire of resistance \(R\) and length \(L\) is cut into 5 equal parts. If these parts are joined parallely, then resultant resistance will be :

A moving coil galvanometer with coil resistance \(G=30\text{ }\Omega\), shows full-scale deflection when the current through it is \(20\text{ }\text{mA}\). The galvanometer is converted to an ammeter of range \(3\text{ }\text{A}\) by using a shunt resistance \(S\). The resistance \(S\) is:

(Shift - II Memory Based)

A galvanometer having a coil of resistance \(30\Omega\) need 20 mA of current for full-scale deflection. If a maximum current of 3 A is to be measured using this galvanometer, the resistance of the shunt to be added to the galvanometer should be \(\frac{30}{X}\Omega\), where\(X\) is

[JEE Main 2025, 23 Jan (Shift 2)]

A moving coil galvanometer with coil resistance \(G=30\text{ }\Omega\), shows full-scale deflection when the current through it is \(20\text{ }\text{mA}\). The galvanometer is converted to an ammeter of range \(3\text{ }\text{A}\) by using a shunt resistance \(S\). The resistance \(S\) is:

(Shift - II Memory Based)

A voltmeter with internal resistance of x \(\Omega\) can be used to measure upto 20 V. In order to increase its measuring range to 30 V , the required modification is to______.

[04 April, 2026 (Shift-I)]

With the help of a potentiometer, we can determine the value of emf of a given cell. The sensitivity of the potentiometer
A. is directly proportional to the length of the potentiometer wire

B. is directly proportional to the potential gradient of the wire
C. is inversely proportional to the potential gradient of the wire
D. is inversely proportional to the length of the potentiometer wire

Choose the correct option for the above statements:

[JEE Main 2023, 29 Jan (Shift 2)]

What equal length of an iron wire and a copper-nickel alloy wire, each of 2 mm diameter connected parallel to give an equivalent resistance of \(3\Omega\) ? (Given resistivities of iron and copper-nickel alloy wire are \(12\mathrm{μΩ}\mathrm{cm}\) and \(51\mathrm{μΩ}\mathrm{cm}\) respectively)

[JEE Main 2021, 26 Aug (Shift 1)]

Ratio of thermal energy released in two resistors R and 3R connected in parallel in an electric circuit is :

[JEE Main 2023, 29 Jan (Shift 1)]

A wire of \(1\Omega\) has a length of \(1\mathrm{m}\). It is stretched till its length increases by \(25\%\). The percentage change in resistance to the nearest integer is:

[JEE Main 2021, 26 Feb (Shift 2)]

The solids which have the negative temperature coefficient of resistance are:

The resistance of a conductor at \(15^\circ C\) is \(16\Omega\) and at \(100^\circ C\) is \(20\Omega\). What will be the temperature coefficient of resistance of the conductor ?

[JEE Main 2021, 27 Jul (Shift 2)]

A wire of a certain material is stretched slowly by ten per cent. Its new resistance and specific resistance become respectively:

What equal length of an iron wire and a copper-nickel alloy wire, each of 2 mm diameter connected parallel to give an equivalent resistance of \(3\Omega\) ? (Given resistivities of iron and copper-nickel alloy wire are \(12\mu \Omega cm\) and \(51\mu \Omega cm\) respectively)

[JEE Main 2021, 26 Aug (Shift 1)]

A capacitor is connected to a 20V battery through a resistance of \(10\Omega\). It is found that the potential difference across the capacitor rises to 2V in \(1\mu s\). The capacitance of the capacitor is ______ \(\mu F\). Given \(\ln \left(\frac{10}{9}\right)=0.105\)

[JEE Main 2021, 1 Sep (Shift 2)]

In the experiment of Ohm's law, a potential difference of \(5.0\mathrm{V}\) is applied across the end of a conductor of length \(10.0\mathrm{cm}\) and diameter of \(5.00\mathrm{mm}\). The measured current in the conductor is \(2.00\mathrm{A}\). The maximum permissible percentage error in the resistivity of the conductor is:

[JEE Main 2021, 18 Mar (Shift 1)]

Two identical heater filaments are connected first in parallel and then in series. At the same applied voltage, the ratio of heat produced in same time for parallel to series will be:

[JEE Main 2023, 11 Apr (Shift 1)]

Given below are two statements: One is labelled as Assertion \(A\) and the other is labelled as Reason \(R\).
Assertion \(A\) : For measuring the potential difference across a resistance of \(600 \Omega\), the voltmeter with resistance \(1000 \Omega\), will be preferred over voltmeter with resistance \(4000 \Omega\).
Reason \(R\) : Voltmeter with higher resistance will draw smaller current than voltmeter with lower resistance.
In the light of the above statements, choose the most appropriate answer from the options given below.

[JEE Main 2023, 1 Feb (Shift 2)]

The H amount of thermal energy is developed by a resistor in 10s when a current of 4A is passed through it. If the current is increased to 16A the thermal energy developed by the resistor in 10s will be:

[JEE Main 2023, 31 Jan (Shift 2)]

Consider a galvanometer shunted with \( 5 \Omega \) resistance and \( 2 \% \) of current passes through it. What is the resistance of the given galvanometer?

[JEE Main 2021, 31 Aug (Shift 1)]

A uniform metallic wire carries a current 2A, when 3.4 V battery is connected across it. The mass of uniform metallic wire is 8.92 × 10^-3kg, density is 8.92 × 10³ kg/m³ and resistivity is 1.7 × 10^-8 \(\Omega\)-m . The length of wire is :

[JEE Main 2023, 25 Jan (Shift 1)]

A current of 5 A is passing through a non-linear magnesium wire of cross - section 0.04m². At every point the direction of current density is at an angle of 60° with unit vector of area of cross -section. The magnitude of electric field at every point of the conductor is : (Resistivity of magnesium \(\rho =44\times {10}^{-8}\Omega m\))

A current of 10 A exists in a wire of cross-sectional area of \(5m{m}^{2}\) with a drift velocity of \(2\times {10}^{-3}m{s}^{-1}\). The number of free electrons in each cubic meter of the wire

If you are provided a set of resistances \(2\Omega ,4\Omega ,6\Omega\) and \(8\Omega\). Connect these resistances so as to obtain an equivalent resistance of \(\frac{46}{3}\Omega\).

[JEE Main 2021, 26 Aug (Shift 2)]

The resistance of platinum wire at \(0^{\circ} \mathrm{C}\) is \(2 \Omega\) and 6.8 \(\Omega\) at \(80^{\circ} \mathrm{C}\). The temperature coefficient of resistance of the wire is :

[NEET 2023]

The charge flowing in a conductor changes with time as \(\mathbf{Q}(\mathbf{t})=\boldsymbol{\alpha t}-\boldsymbol{\beta} \mathbf{t}^{\mathbf{2}}+\boldsymbol{\gamma} \mathbf{t}^{\mathbf{3}}\). Where \(\boldsymbol{\alpha}, \boldsymbol{\beta}\) and \(\boldsymbol{\gamma}\) are constants. Minimum value of current is :

Due to cold weather a \(1 m\) water pipe of cross-sectional area \(1 cm ^2\) is filled with ice at \(-10{ }^{\circ} C\). Resistance heating is used to melt the ice. Current of \(0.5 A\) is passed through \(4 k \Omega\) resistance. Assuming that all the heat produced is used for melting, what is the minimum time required?(Given latent heat of fusion ice \(=3.33 \times 10^5 J kg ^{-1}\), specific heat of ice \(=2 \times 10^3 J kg ^{-1}\) and density of ice \(\left.=10^3 kg / m ^3\right)\)

[JEE Main 2021, 1 Sep (Shift 2)]

The H amount of thermal energy is developed by a resistor in 10s when a current of 4A is passed through it. If the current is increased to 16A. the thermal energy developed by the resistor in 10s will be:

[JEE Main 2023, 31 Jan (Shift 2)]

In a metallic conductor, under the effect of applied electric field ,the free electrons of the conductor

[JEE Main 2023, 10 Apr (Shift 2)]

The material filled between the plates of a parallel plate capacitor has resistivity \(200\mathrm{Ωm}\). The value of capacitance of the capacitor is \(2\mathrm{pF}\). If a potential difference of \(40\mathrm{V}\) is applied across the plates of the capacitor, then the value of leakage current flowing out of the capacitor is : (given the value of relative permittivity of material is 50 )

The number of turns of the coil of a moving coil galvanometer is increased in order to increase current sensitivity by 50%. The percentage change in voltage sensitivity of the galvanometer will be:

[JEE Main 2023, 31 Jan (Shift 2)]