Umakant Kondapure, Collin Fernandes, Nipun Bhatia, Vikram Bathula and, Ketki Deshpande Solutions for Chapter: Current Electricity, Exercise 4: Evaluation Test

A battery of $6 \mathrm{V}$ and negligible internal resistance is connected across the diagonally opposite corners of a cubical network consisting of $12$ resistors each of resistance $2 \mathrm{\Omega }$.

The current through the battery is

Figure shows a $10 \mathrm{V}$ potentiometer used for determination of internal resistance of a $1.5 \mathrm{V}$ cell. The balance point of the cell in the open circuit is $76.3 \mathrm{cm}$. When a resistor of $9.5 \mathrm{\Omega }$ is used in the external circuit of the cell, the balance point shifts to $64.8 \mathrm{cm}$ length of the potentiometer wire. The internal resistance of the cell is

Resistors, each of value $2 \mathrm{\Omega }$ are arranged as shown in figure. The equivalent resistance between points $\mathrm{A}$ and $\mathrm{B}$ is

In the network shown in the figure, points $\mathrm{A}$, $\mathrm{B}$ and $\mathrm{C}$ are at potentials of $7 \mathrm{V}$, $0 \mathrm{V}$ and $1 \mathrm{V}$ respectively. Which of the following statements is INCORRECT?

Assertion: In the potentiometer circuit shown in figure $E_1$ and $E_2$ are the e.m.f. of batteries $B_1$ and $B_2$ respectively with $E_1>E_2$. Battery $B_1$ has negligible internal resistance. For a given value of resistor $R$, the balance length is $x$. If the diameter of the potentiometer wire $AB$ is increased, the balance length $x$ will decrease.

Reason: At the balance point, the potential difference between $AD$ due to battery $B_1=E_2$ the e.m.f. of battery $B_2$.

A wire of resistor $R$ is bent into a circular ring of radius $r$. Equivalent resistance between two points $\mathrm{A}$ and $\mathrm{B}$ on its circumference, when angle $AOB$ is $\beta$, can be given by

Three equal resistors, $R \mathrm{\Omega }$ each is connected as shown in the figure. The value of $R$ for which heat generated in the circuit is maximum is

In the given mesh $WXYZW$, each wire is uniform wire of resistance $r=1 \mathrm{\Omega }$. If a wire of resistance $1 \mathrm{\Omega }$ is connected across $\mathrm{WP}$ and a constant potential difference is applied across $WY$, points $X$ and $P$ will be equipotential. Then point $P$ on $YZ$ placed such that