A cell of $emf$ $E$ and internal resistance $r$ is connected in series with an external resistacne $nr.$ Then, the ratio of the terminal potential difference to $emf$ is
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A wire of resistance $20 \Omega$ is divided into $10$ equal parts. A combination of two parts are connected in parallel and so on. Now resulting pairs of parallel combination are connected in series. The equivalent resistance of final combination is_______.0$\Omega$.
The circuit shown in the figure consists of a battery of $emf$ $\varepsilon = 10 \,V$ ; a capacitor of capacitance $C = 1.0$ $ \mu F$ and three resistor of values $R_1 = 2$ $\Omega$ , $R_2 = 2$ $\Omega$ and $R_3 = 1$ $\Omega$ . Initially the capacitor is completely uncharged and the switch $S$ is open. The switch $S$ is closed at $t = 0.$
The figure shows three circuits $I, II$ and $III$ which are connected to a $3\,V$ battery. If the powers dissipated by the configurations $I, II$ and $III$ are $P_1 , P_2$ and $P_3$ respectively, then
A battery of internal resistance $4$ $\Omega$ is connected to the network of resistances as shown. In order to give the maximum power to the network, the value of $R$ (in $\Omega $) should be
Following figure shows cross-sections through three long conductors of the same length and material, with square cross-section of edge lengths as shown. Conductor $B$ will fit snugly within conductor $A$, and conductor $C$ will fit snugly within conductor $B$. Relationship between their end to end resistance is
A wire of resistance $R$ and radius $r$ is stretched till its radius became $r / 2$. If new resistance of the stretched wire is $x R$, then value of $x$ is $\qquad$