B M Sharma Solutions for Chapter: Electrical Measuring Instruments, Exercise 2: Concept application Excercise

The variation of potential difference $V$ with length $l$ in case of two potentiometers $X$ and $Y$ is as shown in the figure. Which of these two will you prefer for comparing the emfs of the two cells and why?

Two unknown resistances $X$ and $Y$ are placed on the left and right gaps of a meter bridge. The null point in the galvanometer is obtained at a distance of $80 \mathrm{c}\mathrm{m}$ from left. A resistance of $100 \mathrm{\Omega }$ is now connected in parallel across $X$. The null point is then found by shifting the sliding contact towards left by $20 \mathrm{c}\mathrm{m}$. Calculate $X$ and $Y$.

In an experiment with a potentiometer, the null point is obtained at a distance of $60 \mathrm{c}\mathrm{m}$ along the wire from the common terminal with a Leclanche cell. When a shunt resistance of $1 \mathrm{\Omega }$ is connected across the cell, the null point shifts to a distance of $30 \mathrm{c}\mathrm{m}$ from the common terminal. What is the internal resistance of the cell?

In the experiment of calibration of voltmeter, a standard cell of emf $1.1 \mathrm{V}$ is balanced against $440 \mathrm{c}\mathrm{m}$ of potentiometer wire. The potential difference across the ends of a resistance is found to balance against $220 \mathrm{c}\mathrm{m}$ of the wire. The corresponding reading of the voltmeter is $0.5 \mathrm{V}$. Find the error in the reading of voltmeter.

The resistance wire $AB$ in the balancing setup shown in the figure is $10 \mathrm{\Omega }$ long. When $AC=40 \mathrm{c}\mathrm{m}$, no deflection occurs in the galvanometer. Find the unknown resistance $R$.

The figure shows a potentiometer arrangement with $R_{\mathrm{AB}}=10 \mathrm{\Omega }$ and rheostat of variable resistance $x$. For $x=0$ null deflection point is found at $20 \mathrm{c}\mathrm{m}$ from $A$. For the unknown value of $x$ null deflection point was at $30 \mathrm{c}\mathrm{m}$ from $A$, then the value of $x$.

A $6 \mathrm{V}$ battery of negligible internal resistance is connected across a uniform wire $AB$ of length $100 \mathrm{c}\mathrm{m}$. The positive terminal of another battery of emf $4 \mathrm{V}$ and internal resistance $1 \mathrm{\Omega }$ is joined to the point $A$ as shown in figure. Take the potential at $B$ to be zero.

(a) What are the potentials at the points $A$ and $C$?

(b) At which point $D$ and of the wire $AB$ the potential is equal to the potential at $C$?

(c) If the points $C$ and $D$ are connected by a wire, what will be the current through it?

(d) If the $4 \mathrm{V}$ battery is replaced by $7.5 \mathrm{V}$ battery, what would be the answers of parts (a) and (b)?

A battery of emf $2 \mathrm{V}$ and negligible internal resistance is connected across a uniform wire of length $10 \mathrm{m}$ and resistance $30 \mathrm{\Omega }$. The appropriate terminals of a cell of emf $1.5 \mathrm{V}$ and internal resistance $1 \mathrm{\Omega }$ is connected to one end of the wire and the other terminal of the cell is connected through a sensitive galvanometer to a slider on the wire. What is the length of the wire that will be required to produce zero deflection of the galvanometer? How will the balancing length change?

(a) When a coil of resistance $5 \mathrm{\Omega }$ is placed in series with the accumulator.

(b) The cell of $1.5 \mathrm{V}$ is shunted with $5 \mathrm{\Omega }$ resistor?