Umakant Kondapure, Collin Fernandes, Nipun Bhatia, Vikram Bathula and, Ketki Deshpande Solutions for Chapter: Current Electricity, Exercise 3: Competitive Thinking

In a potentiometer experiment of a cell of $e.m.f$. $1.25 \mathrm{V}$ gives balancing length of $30 \mathrm{cm}$. If the cell is replaced by another cell, balancing length is found to be $40 \mathrm{cm}$. What is the emf of second cell?

In above circuit if current through$10 \mathrm{\Omega }$  resistors is $2.5 \mathrm{A}$, value of $\mathrm{R}$ is

The effective resistance between $\mathrm{A}$ and $\mathrm{B}$ in the figure is $\frac{7}{12} \mathrm{\Omega }$ if each side of the cube has $1 \mathrm{\Omega }$ resistance. The effective resistance between the same two points, when the link $\mathrm{AB}$ is removed, is 

Two batteries with e.m.f. $12 \mathrm{V}$ and $13 \mathrm{V}$ are connected in parallel across a load resistor of $10 \mathrm{\Omega }.$ The internal resistances of the two batteries are $1 \mathrm{\Omega }$ and $2 \mathrm{\Omega }$ respectively. The voltage across the load lies between:

Assertion: In a metre bridge experiment, null point for an unknown resistance is measured. Now the unknown resistance is placed 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.

Reason: Resistance of a metal increases with increase in temperature. 

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

$\mathrm{A}$, $\mathrm{B}$ and $\mathrm{C}$ are voltmeters of resistance $R$, $1.5R$ and $3R$ respectively as shown in the figure. When some potential difference is applied between $\mathrm{X}$ and $Y$, the voltmeter readings are $V_{\mathrm{A}}$, $V_{\mathrm{B}}$ and $V_{\mathrm{C}}$ respectively, then

Consider the circuit shown in the figure where all the resistances are of magnitude $1 \mathrm{k\Omega }$. If the current in the extreme right resistance $X$ is $1 \mathrm{mA}$  the potential difference between $\mathrm{A}$ and $\mathrm{B}$ is