$A$ student connects a voltmeter,ammeter,and resistance according to the circuit given. If the voltmeter reading is $20\, V$ and the ammeter reading is $4\, A$,then the resistance $R$ will be:

In the given circuit,calculate the value of current in the $4.5\,\Omega$ resistor in $A$.

In the circuit shown,the current through the $8\,\Omega$ resistor is the same before and after connecting the cell $E$. The value of $E$ is .................... $V$.

When a constant voltage is applied across the ends of a metallic wire,the heat produced in the wire will be doubled if:

$A$ wire of cross-section area $A$,length $L_1$,resistivity $\rho_1$ and temperature coefficient of resistivity $\alpha_1$ is connected to a second wire of length $L_2$,resistivity $\rho_2$,temperature coefficient of resistivity $\alpha_2$ and the same area $A$,so that the wires carry the same current. The total resistance $R$ is independent of temperature for small temperature changes if (Thermal expansion effect is negligible):

Three identical batteries are connected in series with a wire of length $L$. The temperature of the wire increases by $T$ in time $t$. If $N$ such batteries are connected in series with a wire of the same material but length $2L$,the temperature increases by the same amount $T$ in the same time $t$. Find the value of $N$.