A potentiometer wire $AB$ as shown is $40 \mathrm{c}\mathrm{m}$ long of resistance $50 \mathrm{\Omega } {\mathrm{m}}^{-1}$; the free end of an ideal voltmeter is touching the potentiometer wire. What should be the velocity of the jockey as a function of time so that reading in voltmeter varies with time as $(2\sin \mathrm{\pi t})$?

For the potentiometer arrangement shown in the figure, the length of wire $AB$ is $100 \mathrm{c}\mathrm{m}$ and its resistance is $9 \mathrm{\Omega }$. Find the length $AC$ for $A$ which the galvanometer $G$ will show zero deflection.

An ammeter $A$ of finite resistance and a resistor $R$ are joined in series to an ideal cell $C$. A potentiometer $P$ is joined in parallel to $R$. The ammeter reading is $I_0$ and the potentiometer reading is $V_0$. $P$ is now replaced by a voltmeter of finite resistance. The ammeter reading now is $I$ and the voltmeter reading is $V$. Then

In the given potentiometer circuit, the length of the wire $AB$ is $3 \mathrm{m}$ and resistance is $R=4.5 \mathrm{\Omega }$. The length $AC$ for no deflection in galvanometer is

A battery of emf ${\epsilon }_0=12 \mathrm{V}$ is connected across a $4 \mathrm{m}$ long uniform wire having resistance $4 \mathrm{\Omega } {\mathrm{m}}^{-1}$. The cells of small emf ${\epsilon }_1=2 \mathrm{V}$ and ${\epsilon }_2=4 \mathrm{V}$ having internal resistances $r_1=2 \mathrm{\Omega }$ and $r_2=6 \mathrm{\Omega }$, respectively, are connected as shown in the figure. If galvanometer shows no deflection at point $N$, the distance of a point $N$ from a point $A$ is equal to

$V_{\mathit{C}}$ is the ideal voltmeter in the figure. Resistance of the resistor shown is $R$. Initially the switch is in position $2$ when charging of the capacitor starts. Initially, the capacitor was uncharged. The switch in the circuit shifts automatically from $2$ to $1$ when $V_C>\frac{2}{3} V$ and goes back to $2$ from $1$ when $V_C<\frac{V}{3}$. The ideal voltmeter reads the voltage across the capacitor as plotted. What is the period $T$ of the waveform in terms of $R$ and $C$?

In the circuit shown, the reading of the ammeter is doubled after the switch is closed. Each resistor has the resistance $R=1 \mathrm{\Omega }$ and the ideal cell has an emf $\epsilon$ of $10 \mathrm{V}$. Then, the ammeter