A resistor $R$ is connected to a parallel combination of two identical batteries each with emf $E$ and an internal resistance $r\mathit{.}$ The potential drop across the resistance $R$ is-

The equivalent resistance between $A$ and $B$ will be (in $\mathrm{\Omega }$)

A wire is in the form of a tetrahedron. The resistance of each edge is $r.$ The equivalent resistances between corners $1–2$ and $1–3$ are respectively-

The equivalent resistance between points $A$ and $B$ is: 

In the question find the resistance between points $1 - 3.$

The effective resistance between points $P$ and $Q$ of the electrical circuit shown in the figure is:

A $100 \mathrm{W}$ bulb $B_1$ and two $60 \mathrm{W}$ bulbs $B_2$ and $B_3$are connected to a $250 \mathrm{V}$source as shown in the figure. Now $W_1$, $W_2$ and $W_3$ are the output powers of the bulbs $B_1$, $B_2$ and $B_{3 }$respectively. Then:

In the circuit shown the readings of the ammeter and voltmeter are $4 \mathrm{A}$and $20 \mathrm{V}$respectively. The meters are non-ideal, then $R$ is