Current Electricity — JEE Advanced PYQs

A metal wire of cross-sectional area $0.5{\mathrm{mm}}^2$ and length 100 m is connected across a battery of e.m.f. 2 V and internal resistance $1\Omega$. The density, atomic mass and electrical conductivity of the metal are …

As shown in the figure, the resistance of a galvanometer $G$ can be found by the half-deflection method. Here the resistance $R_2$ is adjusted such that when the key $K$ is closed the deflection in the galvanometer becomes half of the value as compared to when $K$ is op …

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 $1\Omega$ resistor. The key is closed at time $t=t_0$. Which of the following statement(s) is(are) correct?
[Given: …

The figure shows a circuit having eight resistances of $1\Omega$ each, labelled $R_1$ to $R_8$, and two ideal batteries with voltages ${\epsilon }_1=12V$ and ${\epsilon }_2=6V$.

Which of the following statement(s) is(are) correct?

Two resistances $R_1=X\Omega$ and $R_2=1\Omega$ 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 $0.2mm$ at $A$ to $1mm$ at $B$. A galvanometer (G) connected to the center …

In Circuit-1 and Circuit-2 shown in the figures, $R_1=1\Omega ,R_2=2\Omega$ and $R_3=3\Omega$. $P_1$ 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 …

In order to measure the internal resistance $r_1$ of a cell of emf E, a meter bridge of wire resistance $R_0=50\Omega$, a resistance $R_0/2$, another cell of $\mathrm{emf}E/2$ (internal resistance $r$ ) and a galvanometer $G$ are used in a circuit, a …

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 ${\mathrm{q}}_1\mu$C. Then S is switched to position Q. After a long time, the charge on the capacitor is ${\mathrm{q}}_2\mu$C.

The magnitude of …

Shown in the figure is a semicircular metallic strip that has thickness t and resistivity $\rho$. Its inner radius is ${\mathrm{R}}_1$ and outer radius is ${\mathrm{R}}_2$. If a voltage ${\mathrm{V}}_0$ is applied between its two ends, a current I flows in it. In addition, it is …

In the balanced condition, the values of the resistances of the four arms of a Wheatstone bridge are shown in the figure below. The resistance $R_3$ has temperature coefficient $0.0004°{\text{C}}^{-1}$. If the temperature of $R_3$ is increased by $100°\text{C}$, the voltage develo …

Two identical moving coil galvanometer have $10\Omega$ resistance and full scale deflection at $2\mu \mathrm{A}$ 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 …

A moving coil galvanometer has 50 turns and each turn has an area $2\times 10^{-4}{m}^2$. The magnetic field produced by the magnet inside the galvanometer is $0.02T$. The torsional constant of the suspension wire is $10^{-4}Nmra{d}^{-1}$. When a current flows through t …

Consider a simple $RC$ circuit as shown in Figure 1.

Process 1: In the circuit the switch $S$ is closed at $t=0$ and the capacitor is fully charged to voltage $V_0$ (i.e., charging continues for time $T\gg RC$). In the process some dissipation $\left(E_D\right)$ …

Consider a simple $RC$ circuit as shown in Figure 1.

Process 1: In the circuit the switch $S$ is closed at $t=0$ and the capacitor is fully charged to voltage $V_0$ (i.e., charging continues for time $T\gg RC$). In the process some dissipation $\left(E_D\right)$ …

An infinite line charge of uniform electric charge density $\lambda$ 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 $\epsilon$ and electr …

Consider two identical galvanometers and two identical resistors with resistance $R$. If the internal resistance of the galvanometers $R_{\mathrm{C}}<R/2$, which of the following statement(s) about any one of the galvanometers is(are) true?

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

PARAGRAPH 2

Consider an evacuated cylindrical chamber of height $h$ having rigid conducting plates at the ends and an insulating curved surface as shown in the figure. A number of spherical balls made of a light weight and soft material and coated with a conducting material ar …

In an aluminum (AI) 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 AI and Fe are $2.7\times 10^{-8}\Omega \mathrm{m}$ and $1.0\times 10^{-7}\Omega \mathrm{m}$, respectively. The elec …

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

During an experiment with a metre bridge, the galvanometer shows a null point when the jockey is pressed at $40.0cm$ using a standard resistance of $90\Omega$, as shown in the figure. The least count of the scale used in the metre bridge is 1 $mm$. The unknown resistance …

Heater of an electric kettle is made of a wire of length $L$ and diameter $d$. It takes 4 minutes to raise the temperature of 0.5kg water by 40K. This heater is replaced by a new heater having two wires of the same material, each of length $L$ and diameter $2d$. The way t …

Two ideal batteries of $emf{V}_1$ and $V_2$ and three resistances $R_1,R_2$ and $R_3$ are connected as shown in the figure. The current in resistance $R_2$ would be zero if

A galvanometer gives full scale deflection with $0.006A$ current. By connecting it to a 4990 $\Omega$ resistance, it can be converted into a voltmeter of range $0-30V$. If connected to a $\frac{2n}{249}\Omega$ resistance, it becomes an ammeter of range $0-1.5A$. Th …

Paragraph for Questions 15 and 16

A thermal power plant produces electric power of $600kW$ at $4000V$, which is to be transported to a place 20 km away from the power plant for consumers' usage. It can be transported either directly with a cable of large current carrying c …

For the resistance network shown in the figure, choose the correct option(s).

A meter bridge is set-up as shown, to determine an unknown resistance 'X' using a standard 10 ohm resistor. The galvanometer shows null point when tapping-key is at 52 cm mark. The end-corrections are 1 cm and 2 cm respectively for the ends A and B. The determined value of 'X' is

Two batteries of different emfs and different internal resistances are connected as shown. The voltage across AB in volts is

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

Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with the increase in temperature. If at room temperature, $100\mathrm{W},60\mathrm{W}$ and 40 W bulbs have filament resistances ${\mathrm{R}}_{100},{\mathrm{R}}_{60}$ and …

To verify Ohm's law, a student is provided with a test resistor ${\mathrm{R}}_{\mathrm{T}}$, a high resistance ${\mathrm{R}}_1$, a small resistance ${\mathrm{R}}_2$, two identical galvanometers ${\mathrm{G}}_1$ and ${\mathrm{G}}_2$, and a variable voltage source V. The co …

When two identical batteries of internal resistance $1\Omega$ each are connected in series across a resistor R, the rate of heat produced in R is $J_1$. When the same batteries are connected in parallel across R, the rate is $J_2$. If $J_1=2.25J_2$ then the value of R i …

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 seconds) does the voltage across them become 4 V ?
[Take : $\ell n5=1.6,\ell n3=1.1$ ]

For the circuit shown in the figure

Figure shows three resistor configurations R1, R2 and R3 connected to 3 V battery. If the power dissipated by the configuration R1, R2 and R3 is P1, P2 and P3, respectively, then

STATEMENT-1
In a Meter Bridge experiment, null point for an unknown resistance is measured. Now, the unknown resistance is put inside an enclosure maintained at a higher temperature. The null point can be obtained at the same point as before by decreasing the value of the standar …

A resistance of $2\Omega$ is connected across one gap of a metre-bridge (the length of the wire is 100 cm) and an unknown resistance, greater than $2\Omega$, is connected across the other gap. When these resistances are interchanged, the balance point shifts by 20 cm. Negle …

Given,


(I)

(II)

(III)

The time constants (in $\mu \mathrm{S}$) for the circuits I, II, III are respectively

The capacitor of capacitance C can be charged (with the help of a resistance R) by a voltage source V, by closing switch ${\mathrm{S}}_1$ while keeping switch ${\mathrm{S}}_2$ open. The capacitor can be connected in series with an inductor 'L' by closing switch …