Current Electricity · Physics · JEE Advanced

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

In the following circuit $C_{1}=12 \mu F, C_{2}=C_{3}=4 \mu F$ and $C_{4}=C_{5}=2 \mu F$. The charge stored in $C_{3}$ is ____________ $\mu C$.

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

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 J₁. When the same batteries are connected in parallel across R, the rate is J₂. If J₁ = 2.25 J₂, then the value of R in $$\Omega$$ is __________.

The figure shows a circuit having eight resistances of $1 \Omega$ each, labelled $R_{1}$ to $R_{8}$, and two ideal batteries with voltages $\varepsilon_{1}=12 \mathrm{~V}$ and $\varepsilon_{2}=6 \mathrm{~V}$.

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

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

For the circuit shown in the figure

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

If the direct transmission method with a cable of resistance 0.4 $$\Omega$$ km^$$-$$1 is used, the power dissipation (in %) during transmission is

A meter bridge is set up as shown, to determine an unknown resistance X using a standard 10 $$\Omega$$ 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

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, 60 and 40 W bulbs have filament resistances R₁₀₀, R₆₀ and R₄₀ respectively, the relation between these resistances is

To verify Ohm's law, a student is provided with a test resitor R_T, a high resistance R₁, a small resistance R₂, two identical galvanometers G₁ and G₂, and a variable voltage source V. The correct circuit to carry out the experiment is

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

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 standard resistance.

and

STATEMENT - 2

Resistance of a metal increases with increase in temperature.