Current Electricity — JEE Main PYQs

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.

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 ____________.

The voltage and the current between $A$ and $B$ points shown in the circuit are ____________.

Multi-branch circuit between points $A$ and $B$: three parallel horizontal branches each with a battery (27 V + 3 Ω, 27 V + 3 Ω, and 14 V + 13 V in series + 3 Ω), a diagonal branch from $A$ with 27 V battery and two 3 Ω resistors, and a bottom branch with a 3 Ω resistor

Refer to the figure given below. The values of $I_1$, $I_2$ and $I_3$ are ________.

A diamond-shaped circuit. Left branch: a 10 V battery in series with a 1 Ω resistor carrying current $I_1$ (horizontal middle branch). Upper-left arm has a 4 Ω resistor, upper-middle a 2 Ω resistor with current $I_2$ leaving the top node toward a 5 V battery on the right vertex. Lower-left arm has a 4 Ω resistor carrying current $I_3$, and a 2 Ω resistor in the lower-middle branch.

Refer to the figure given below, current between terminals $A$ and $B$ is __________ A.

A ladder network between terminals $A$ (bottom left) and $B$ (bottom right) with four parallel horizontal rows. Each of the top three rows contains three series cells of 5 V each, each cell in series with a 3 Ω resistor (three cells and three 3 Ω resistors per row). The bottom row contains three 3 Ω resistors in series with no cells.

Under steady state condition the potential difference across the capacitor in the circuit is ________ V.

circuit with three parallel branches — top branch: $2\ \Omega$ resistor; middle branch: $2\ \mu\text{F}$ capacitor in series with $4\ \Omega$ resistor; bottom branch: $2 \text{ V}$ battery in series with $6\ \Omega$ resistor

When an external resistance of $5\ \Omega$ is connected across terminals of a cell, a current of $0.25 \text{ A}$ flows through it. When the $5\ \Omega$ resistor is replaced by a $2\ \Omega$ resistor, a current of $0.5 \text{ A}$ flows through it. The internal resistance of the cell is __________ $\Omega$.

Refer to the circuit diagram given below. The heat generated across the 6 $\Omega$ resistance in 100 second is $\frac{\alpha}{100}$ J. The value of $\alpha$ is ________. (Nearest integer)

A circuit with two loops: the upper branch has a 6 $\Omega$ resistor in series with a 3 V battery; a parallel branch has a 4 $\Omega$ resistor; the outer loop contains a 3 $\Omega$ resistor and a 2 V battery

A moving coil of galvanometer when shunted with 2 $\Omega$ resistance gives a full scale deflection for a current of 500 mA. When a resistance of 470 $\Omega$ is connected in series it gives a full scale deflection for 10 V potential applied on it. The value of resistance of galvanometer coil is _________ $\Omega$.

Two cells of emfs 1 V and 2 V and internal resistance 2 $\Omega$ and 1 $\Omega$, respectively connected in parallel, gave a current of 1 A through an external resistance. If the polarity of one cell is reversed, then value of current through the external resistance will be $\dfrac{\alpha}{5}$ A. The value of $\alpha$ is ________.

The stored charge in the capacitor in steady state of the following circuit is ________ $\mu\text{C}$.

circuit with a 12 V battery on the left; top row series resistors $5\,\Omega$, $4\,\Omega$, $10\,\Omega$; vertical parallel branches of $12\,\Omega$, $10\,\Omega$, $4\,\Omega$; bottom row series resistors $2\,\Omega$, $2\,\Omega$; a $100\,\mu\text{F}$ capacitor at the far right end

The battery of a mobile phone is rated as 4.2 V, 5800 mAh. How much energy is stored in it when fully charged ?

A wire of length 25 m and cross-sectional area 5 $\mathrm{mm^2}$ having resistivity of $2 \times 10^{-6} \ \Omega$ m is bent into a complete circle. The resistance between diametrically opposite points will be

In the figure shown below, a resistance of 150.4 $\Omega$ is connected in series to an ammeter A of resistance 240 $\Omega$. A shunt resistance of 10 $\Omega$ is connected in parallel with the ammeter. The reading of the ammeter is __________ mA.

a 20 V battery in series with a 150.4 Ω resistor and an ammeter A; a 10 Ω shunt resistor is connected in parallel with the ammeter

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

Two cells of emfs 1 V and 2 V and internal resistances $2\ \Omega$ and $1\ \Omega$, respectively, are connected in series with an external resistance of $6\ \Omega$. The total current in the circuit is $I_1$. Now the same two cells in parallel configuration are connected to same external resistance. In this case, the total current drawn is $I_2$. The value of $\left(\frac{I_1}{I_2}\right)$ is $\frac{x}{3}$. The value of $x$ is __________.

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 mains supply. The total power drawn by the combination is :

From the combination of resistors with resistances values $\mathrm{R_1} = \mathrm{R_2} = \mathrm{R_3} = 5 \mathrm{~\Omega}$ and $\mathrm{R_4} = 10 \mathrm{~\Omega}$, which of the following combination is the best circuit to get an equivalent resistance of $6 \mathrm{~\Omega}$ ?

[Options are circuit figures]

A wire of resistance R is bent into a triangular pyramid as shown in figure with each segment having same length. The resistance between points A and B is R/n. The value of n is :

a triangular pyramid (tetrahedron) network of six equal resistive wire segments, with vertices A and B at the two ends of the base edge

Which of the following resistivity ($\rho$) v/s temperature (T) curves is most suitable to be used in wire bound standard resistors ?

Given below are two statements :

Statement I : The equivalent emf of two non-ideal batteries connected in parallel is smaller than the emf of either of the two batteries.

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 :

Sliding contact of a potentiometer is in the middle of the potentiometer wire having resistance $R_p = 1\,\Omega$ as shown in the figure. An external resistance of $R_e = 2\,\Omega$ is connected via the sliding contact. The electric current in the circuit is :

a 0.9 V cell connected across a potentiometer wire of resistance $R_p = 1\,\Omega$; an external resistance $R_e = 2\,\Omega$ is connected between the sliding contact (at the middle of the wire) and one end of the wire

At steady state the charge on the capacitor, as shown in the circuit below, is __________ $\mu\mathrm{C}$.

circuit with an $8~\mu\mathrm{F}$ capacitor connected in parallel with a $10~\Omega$ resistor; this combination is in series with a $15~\Omega$ resistor and a 5 V battery

A wire of resistance 9 $\Omega$ is bent to form an equilateral triangle. Then the equivalent resistance across any two vertices will be _____ ohm.

A wire of resistance R is bent into an equilateral triangle and an identical wire is bent into a square. The ratio of resistance between the two end points of an edge of the triangle to that of the square is

Find the equivalent resistance between two ends of the following circuit

circuit between two terminals — three resistors each of value $r/3$: two in series along the lower branch, with a plain wire bridging across the first two, and the third resistor ($r/3$) in the right portion, with connecting wire loops above and below

The value of current I in the electrical circuit as given below, when potential at A is equal to the potential at B, will be __________ A.

a Wheatstone-bridge-like network. Current I enters a node splitting into two branches: the top branch has $10\,\Omega$ then node A then $20\,\Omega$; the bottom branch has R then node B then $40\,\Omega$. A $30\,\Omega$ resistor connects A to B (bridge arm). The two branches recombine and current I exits. The network is driven by a 40 V battery with key K.

The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are $8~\Omega$ and $10~\Omega$ respectively. After inserting in a hot bath of temperature 400°C, the resistance of platinum wire is :

Twelve wires each having resistance 2 Ω are joined to form a cube. A battery of 6 V emf is joined across point a and c. The voltage difference between e and f is ________ V.

a cube with top face vertices a, b, c, d and bottom face vertices e, h, g, f (e below a, f below d, g below c, h below h-corner); a 6 V battery connected across the face diagonal between vertices a and c of the top face

An electric bulb rated $50~W$ - $200~V$ is connected across a $100~V$ supply. The power dissipation of the bulb is:

Two wires $A$ and $B$ are made up of the same material and have the same mass. Wire $A$ has radius of $2.0~mm$ and wire $B$ has radius of $4.0~mm$. The resistance of wire $B$ is $2\Omega$. The resistance of wire $A$ is ______ $\Omega$.

In the given figure $R_1 = 10\,\Omega$, $R_2 = 8\,\Omega$, $R_3 = 4\,\Omega$ and $R_4 = 8\,\Omega$. Battery is ideal with emf 12V. Equivalent resistant of the circuit and current supplied by battery are respectively :

circuit with a 12 V battery; $R_1$ in the top branch, and $R_2$, $R_4$ and $R_3$ connected in parallel between the two nodes

The electric field between the two parallel plates of a capacitor of $1.5\ \mu\mathrm{F}$ capacitance drops to one third of its initial value in $6.6\ \mu\mathrm{s}$ when the plates are connected by a thin wire. The resistance of this wire is ________ $\Omega$. (Given, $\log 3 = 1.1$)

The ratio of heat dissipated per second through the resistance $5\ \Omega$ and $10\ \Omega$ in the circuit given below is :

a 10 V battery connected to a $20\ \Omega$ resistor in series with a parallel combination of $5\ \Omega$ and $10\ \Omega$ resistors

A wire of resistance $20\ \Omega$ is divided into 10 equal parts, resulting pairs. A combination of two parts are connected in parallel and so on. Now resulting pairs of parallel combination are connected in series. The equivalent resistance of final combination is ________ $\Omega$.

The value of unknown resistance $(x)$ for which the potential difference between $B$ and $D$ will be zero in the arrangement shown, is :

Wheatstone-bridge-like network between A and C. Upper-left arm A to B: $24\,\Omega$ in parallel with series $12\,\Omega$ and $12\,\Omega$; upper-right arm B to C: $1\,\Omega$ in parallel with $1\,\Omega$; lower-left arm A to D: $x\,\Omega$ in parallel with series $12\,\Omega$ and $12\,\Omega$; lower-right arm D to C: $0.5\,\Omega$; battery of $14.5\,V$ connected across A and C

A wire of resistance $R$ and radius $r$ is stretched till its radius became $r/2$. If new resistance of the stretched wire is $x\,R$, then value of $x$ is _________.

The number of electrons flowing per second in the filament of a 110 W bulb operating at 220 V is : (Given $e = 1.6 \times 10^{-19}\ \mathrm{C}$)

In the given figure an ammeter A consists of a 240 Ω coil connected in parallel to a 10 Ω shunt. The reading of the ammeter is ________ mA.

series circuit with a 140.4 Ω resistor, a 24 V battery, and the ammeter A

In the given circuit, the terminal potential difference of the cell is :

circuit with a 3 V cell of internal resistance 1 Ω connected across two parallel 4 Ω resistors

Resistance of a wire at 0 °C, 100 °C and t °C is found to be $10\ \Omega$, $10.2\ \Omega$ and $10.95\ \Omega$ respectively. The temperature t in Kelvin scale is ________.

Water boils in an electric kettle in 20 minutes after being switched on. Using the same main supply, the length of the heating element should be ________ to ________ times of its initial length if the water is to be boiled in 15 minutes.

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 $10\ \Omega$ and a resistance R, to a 100 V mains as shown in figure. For the heater to operate at 62.5 W, the value of R should be _________ $\Omega$.

a 100 V source in series with a $10\ \Omega$ resistor feeding points B and C; between B and C the heater and resistance R are connected in parallel

The equivalent resistance between A and B is :

resistor network between terminals A and B: top row has 6 Ω and 10 Ω in series; left side has 8 Ω and 4 Ω; right side has 5 Ω and 7 Ω; bottom row has 11 Ω and 8 Ω in series; a middle vertical branch crosses over the horizontal middle wire

A galvanmeter has a coil of resistance $200\ \Omega$ with a full scale deflection at $20\ \mu\mathrm{A}$. The value of resistance to be added to use it as an ammeter of range (0-20) mA is :

The current flowing through the $1\ \Omega$ resistor is $\dfrac{n}{10}$ A. The value of n is ________.

diamond-shaped circuit A-B-C-D-E: a 10 V battery with 4 Ω and 1 Ω resistors on branch A to C (current I₁ marked through the 1 Ω), a 2 Ω resistor from B to C and another 2 Ω from C to D, 4 Ω on branch A to D, and a 5 V battery at E on the right connecting B and D

The effective resistance between $A$ and $B$, if resistance of each resistor is $R$, will be :

resistor network — from A a resistor R leads to a diamond of resistors (two R in the upper arms, two R in the lower arms) with two vertical bridge resistors R and two horizontal middle resistors R meeting at the centre, then a resistor R leads to B

At room temperature ($27°C$), the resistance of a heating element is $50~\Omega$. The temperature coefficient of the material is $2.4\times10^{-4}~°C^{-1}$. The temperature of the element, when its resistance is $62~\Omega$, is ________ $°C$.

The reading in the ideal voltmeter (V) shown in the given circuit diagram is :

a closed loop containing, in the top branch, three cells of 5V each with internal resistance 0.2 Ω each; in the left branch one 5V cell with 0.2 Ω; in the bottom branch three 5V cells with 0.2 Ω each; on the right, a 5V cell with 0.2 Ω connected across an ideal voltmeter (V)

The current in a conductor is expressed as $I = 3t^2 + 4t^3$, where I is in Ampere and t is in second. The amount of electric charge that flows through a section of the conductor during t = 1s to t = 2s is ________ C.

A galvanometer (G) of $2\ \Omega$ resistance is connected in the given circuit. The ratio of charge stored in $\mathrm{C_1}$ and $\mathrm{C_2}$ is :

a bridge circuit powered by a 6 V battery; one pair of opposite arms has resistors $4\ \Omega$ and $6\ \Omega$, the other pair has capacitors $C_1 = 4\ \mu F$ and $C_2 = 6\ \mu F$, with galvanometer G across the middle

To measure the temperature coefficient of resistivity $\alpha$ of a semiconductor, an electrical arrangement shown in the figure is prepared. The arm BC is made up of the semiconductor. The experiment is being conducted at 25°C and resistance of the semiconductor arm is 3 m$\Omega$. Arm BC is cooled at a constant rate of 2°C/s. If the galvanometer G shows no deflection after 10 s, then $\alpha$ is :

Wheatstone bridge ABCD with arm AB = 0.8 m$\Omega$, arm AD = 1 m$\Omega$, arm DC = 3 m$\Omega$, arm BC the semiconductor, galvanometer G across the middle, supply V = 5 mV

In an electrical circuit drawn below the amount of charge stored in the capacitor is ________ $\mu$C.

a 10 V battery in series with $R_1 = 4\ \Omega$; a branch with capacitor $C = 10\ \mu F$ in series with $R_2 = 5\ \Omega$ connected in parallel with $R_3 = 6\ \Omega$

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 :

The charge accumulated on the capacitor connected in the following circuit is ________ $\mu$C.

(Given $C = 150\ \mu$F)

Wheatstone-bridge circuit driven by a 10 V battery; upper branch has $R_1 = 1\ \Omega$ then $R_3 = 6\ \Omega$, lower branch has $R_2 = 2\ \Omega$ then $R_4 = 4\ \Omega$; capacitor C is connected between the midpoints A (between $R_1$ and $R_2$) and B (between $R_3$ and $R_4$)

The electric current through a wire varies with time as $I = I_0 + \beta t$, where $I_0 = 20$ A and $\beta = 3$ A/s. The amount of electric charge crossed through a section of the wire in 20 s is :

A $16\,\Omega$ wire is bend to form a square loop. A 9V battery with internal resistance $1\,\Omega$ is connected across one of its sides. If a $4\,\mu F$ capacitor is connected across one of its diagonals, the energy stored by the capacitor will be $\frac{x}{2}\ \mu J$, where $x =$ __________.

An electric toaster has resistance of $60~\Omega$ at room temperature ($27~°\mathrm{C}$). The toaster is connected to a 220 V supply. If the current flowing through it reaches 2.75 A, the temperature attained by toaster is around : ( if $\alpha = 2 \times 10^{-4}/°\mathrm{C}$)

A potential divider circuit is shown in figure. The output voltage $\mathrm{V}_0$ is :

a 4 V battery across a series chain of a $3.3~\mathrm{k}\Omega$ resistor followed by seven $100~\Omega$ resistors; $\mathrm{V}_0$ is taken across the last six $100~\Omega$ resistors (tap after the first two resistors)

Two cells are connected in opposition as shown. Cell $\mathrm{E}_1$ is of 8 V emf and $2~\Omega$ internal resistance; the cell $\mathrm{E}_2$ is of 2 V emf and $4~\Omega$ internal resistance. The terminal potential difference of cell $\mathrm{E}_2$ is ________ V.

a closed loop with cells $\mathrm{E}_1$ and $\mathrm{E}_2$ connected in opposition between points A, B and C

When a potential difference $V$ is applied across a wire of resistance $R$, it dissipates energy at a rate $W$. If the wire is cut into two halves and these halves are connected mutually parallel across the same supply, the energy dissipation rate will become:

Two resistance of $100\ \Omega$ and $200\ \Omega$ are connected in series with a battery of $4\ V$ and negligible internal resistance . A voltmeter is used to measure voltage across $100\ \Omega$ resistance, which gives reading as $1\ V$. The resistance of voltmeter must be _______ $\Omega$.

Two conductors have the same resistances at $0°\mathrm{C}$ but their temperature coefficients of resistance are $\alpha_1$ and $\alpha_2$. The respective temperature coefficients for their series and parallel combinations are :

Equivalent resistance of the following network is ________ $\Omega$.

resistor network between terminals A and B — three parallel branches ($R_1$ 6 $\Omega$ shown with $R_2$, $R_3$ 2 $\Omega$, and $R_5$ 3 $\Omega$ with $R_6$ 3 $\Omega$) linked by series resistors of 2 $\Omega$ ($R_2$ top-left) and 2 $\Omega$ ($R_4$ top-right)

By what percentage will the illumination of the lamp decrease if the current drops by 20%?

In the following circuit, the battery has an emf of 2V and an internal resistance of $\frac{2}{3}\ \Omega$. The power consumption in the entire circuit is ________ W.

a square network of $2\ \Omega$ resistors — four resistors along the sides/diagonals meeting at the center and one $2\ \Omega$ resistor at the bottom, connected to a 2 V battery with internal resistance $\frac{2}{3}\ \Omega$