In the given circuit,for maximum power to be transferred from a battery with an internal resistance of $4\, \Omega$,what should be the value of $R$ in $\Omega$?

Two batteries of e.m.f $4 \text{ V}$ and $8 \text{ V}$ with internal resistance $1 \Omega$ and $2 \Omega$ respectively are connected in a circuit with a resistance of $9 \Omega$ as shown in the figure. The current and potential difference between the points $P$ and $Q$ is

$A$ straight wire of resistance $R$ is bent into the shape of a square. $A$ cell of emf $12 \text{ V}$ is connected between two adjacent corners of the square. The potential difference across any diagonal of the square is (in $\text{ V}$)

In the given circuit,the current in $8 \Omega$ resistance is $1.5 \text{ A}$. The total current $(I)$ flowing in the circuit is (in $\text{ A}$)

The e.m.f. of a cell is $E \text{ volts}$ and its internal resistance is $r \text{ ohm}$. The resistance in the external circuit is also $r \text{ ohm}$. The potential difference across the cell will be

The charge flowing through a resistance $R$ varies with time $t$ as $Q = at - bt^2$,where $a$ and $b$ are positive constants. The total heat produced in $R$ is