S L Arora Solutions for Chapter: Magnetic Effect of Current, Exercise 4: HOTS Problems on Higher Order Thinking Skills

A given rectangular coil $OLMN$ of area $A$, carrying a given current $I$, is placed in a uniform magnetic field $\overrightarrow{B}=B\hat{k}$, in two different orientations (a) and (b) as
shown. What is the magnitude of torque experienced by this coil in the two cases ?

A coil in the shape of an equilateral triangle of side $0.02 \mathrm{m}$ is suspended from a vertex such that it is hanging in a vertical plane between the pole pieces of permanent magnet producing a horizontal magnetic field $5\times {10}^{-2}$ tesla. Find the couple acting on the coil when a current of $0.1 A$ is passed through it and the magnetic field is parallel to its plane.

In the circuit shown in Figure, a voltmeter reads $30 V$, when it is connected across $400 \mathrm{\Omega }$ resistance. Calculate what the same voltmeter will read, when connected across the $300 \mathrm{\Omega }$ resistance.

A voltmeter of resistance $R_V$ and an ammeter of resistance $R_A$ are connected in a circuit to measure, a resistance R as shown in Figure. The ratio of the meter readings gives an apparent resistance $R\text{'}$. Show that $R$ and $R\text{'}$ are related by the relation

$\frac{1}{R}=\frac{1}{R\text{'}}=\frac{1}{R_V}$.

A length $L$ of a wire carries a current $I$. Show that if the wire is formed into a circular coil, the maximum torque in a given magnetic field is developed when the coil has one turn only and the maximum torque has the value,$\tau =L^{2}IB/4\pi$. 

A galvanometer is shunted by $1/n$th of its resistance. Find the fraction of the total current passing through the galvanometer. 

If a galvanometer is connected in series with a high resistance so that potential drop across the galvanometer is $1/n$th of the total applied voltage, then show
that the combined resistance of the galvanometer and the series resistor is n times the resistance of the galvanometer i.e., $R_V=n{R}_g$.

A galvanometer of resistance $G$ is converted into a voltmeter to measure upto $V$ volts by connecting a resistance $R_1$ in series with the coil. If a resistance $R_2$ is connected in series with it, then it can measure upto $\raisebox{1ex}{$V$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ volts. Find the resistance, in terms of $R_1$ and $R_2$, required to be connected to convert it into a voltmeter that can read upto $2 V$. Also find the resistance $G$ of the galvanometer in terms of $R_1$ and $R_2$.