It is easier to start a car engine on a hot day than on a cold day. This is because the internal resistance of the car battery

$12$ cells,each having the same emf $E$ and internal resistance $r$,are connected in series and kept in a closed box. Some of the cells are wrongly connected. This battery is connected in series with an ammeter and two cells,each identical to the previous cells. The current is $3 \, A$ when the external cells aid the battery and $2 \, A$ when the external cells oppose the battery. How many cells in the battery are wrongly connected?

When two identical batteries of internal resistance $1 \Omega$ each are connected in series across a resistor $R$,the rate of heat produced in $R$ is $P_1$. When the same batteries are connected in parallel across $R$,the rate of heat produced is $P_2$. If $P_1 = 2.25 P_2$,then the value of $R$ is (in $Omega$)

Two cells,having the same $e.m.f.$ $E$,are connected in series through an external resistance $R$. The cells have internal resistances $r_1$ and $r_2$ $(r_1 > r_2)$ respectively. When the circuit is closed,the potential difference across the first cell is zero. The value of $R$ is

Two cells of $emfs$ $E_1$ and $E_2$ and internal resistances $r_1$ and $r_2$ are connected in parallel. The $emf$ and internal resistance of the equivalent source is