Two resistances ${R_1}$ and ${R_2}$ are connected as shown in the figure to two batteries of $e.m.f.$ ${E_1}$ and ${E_2}$. If ${E_2}$ is short-circuited,the current through ${R_1}$ is

The potential difference between point $A$ and $B$ is ............. $V$.

$A$ voltmeter of resistance $150 \Omega$ connected across a cell of e.m.f. $3 \ V$ reads $2.5 \ V$. What is the internal resistance of the cell (in $\Omega$)?

In the circuit shown,the resistance $r$ is a variable resistance. If for $r = fR$,the heat generation in $r$ is maximum,then the value of $f$ is:

$A$ fuse wire of radius $0.2 \,mm$ blows off with a current of $5 \,A$. The fuse wire of the same material but of radius $0.3 \,mm$ will blow off with a current of:

$A$ wire of uniform resistance $\lambda \ \Omega/m$ is bent into a circle of radius $r$. Two radial wires, each of length $r$, are connected from the center $O$ to points $A$ and $B$ on the circumference, where the angle $\angle AOB = 90^\circ$. The equivalent resistance between points $A$ and $B$ is . . . . . . $\Omega$.