In the adjacent circuit, $\mathrm{}AB\mathrm{}$ is a potentiometer wire of length $\mathrm{}40\mathrm{}\mathrm{c}\mathrm{m}\mathrm{}$ and resistance per unit length $\mathrm{}50\mathrm{}\mathrm{\Omega }/\mathrm{m}$ . As shown in the figure, 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 the voltmeter varies with time as $\mathrm{}\left(2\sin \pi t\right)$ ?

In the diagram shown, all the wires have resistance $R$. The equivalent resistance between the upper and lower dots shown in the diagram is

An electric bell has a resistance of $5\Omega$ and requires a current of $0.25 A$ to work it. Assuming that the resistance of the bell wire is $1\Omega$ per $15 \mathrm{m}$ and that the bell push is $90 \mathrm{m}$ distance from the bell. How many cells each of emf $1.4 \mathrm{V}$ and internal resistance $2\Omega$, will be required to work the circuit

A wire has resistance of $24 \mathrm{\Omega }$ is bent in the following shape. The effective resistance between $A$ and $B$ is