Embibe Experts Solutions for Chapter: Current Electricity, Exercise 1: JEE Advanced Paper 2 - 2020

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 $0.0004°{\mathrm{C}}^{-1}$. If the temperature of $R_3$ is increased by $100°\mathrm{C},$ the voltage developed between $S$ and $T$ will be $n \mathrm{V}$. Write the value of $100n$ to the nearest integer.

Shown in the figure is a semicircular metallic strip that has thickness $t$ and resistivity $\rho$. 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 $\mathrm{\Delta }V$ 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)

In an aluminum (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 $2.7\times {10}^{-8}\mathrm{\Omega }\mathrm{ }\mathrm{m}$ and $1.0\times {10}^{-7}\mathrm{\Omega }\mathrm{ }\mathrm{m}$ , respectively. The electrical resistance between the two faces P and Q of the composite bar is

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 $0.5\mathrm{kg}$ water by $40 \mathrm{K}$. This heater is replaced by a new heater having two wires of the same material, each of length $L$ and diameter $2d$. The way these wires are connected is given in the options. How much time in minutes will it take to raise the temperature of the same amount of water by $40 \mathrm{K}$?

Two ideal batteries of emf ${\mathrm{V}}_1$ and ${\mathrm{V}}_2$ and three resistances ${\mathrm{R}}_1,\mathrm{ }{\mathrm{R}}_2$ and ${\mathrm{R}}_3$ are connected as shown in the figure. The current in resistance ${\mathrm{R}}_2$ would be zero if