An external resistance $R$ is connected to a battery of $e.m.f.$ $V$ and internal resistance $r$. The joule heat produced in resistor $R$ is maximum when $R$ is equal to

$A$ car has a fresh battery of $e.m.f.$ $12\, V$ and internal resistance of $0.05\, \Omega$. If the starter motor draws a current of $90\, A$,the terminal voltage when the starter is on will be ............... $V$.

When two identical resistors are connected in series to an ideal cell,the current through each resistor is $2 \ A$. If the resistors are connected in parallel to the same cell,the current through each resistor is: (in $A$)

Two equal resistances,$400 \Omega$ each,are connected in series with an $8 V$ battery. If the resistance of the first one increases by $0.5 \%$,what is the change required in the resistance of the second one in order to keep the potential difference across it unaltered?

The potential difference across $A B$ in the network shown is .........

$A$ current of $6\, A$ enters at corner $P$ of an equilateral triangle $PQR$ having $3$ wires of resistance $2 \,\Omega$ each and leaves by the corner $R$. The current $i_{1}$ in ampere is ........ .