A wire of length $5\,m$ and radius $1\,mm$ has a resistance of $1\, ohm$. What length of the wire of the same material at the same temperature and of radius $2\,mm$ will also have a resistance of $1\, ohm$ .............. $m$
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$n$ identical bulbs, each designed to draw a power $p$ from a certain voltage supply, are joined in series across that supply. The total power which they will draw 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
A cell $E _{1}$ of $emf 6 V$ and internal resistance $2 \Omega$ is connected with another cell $E _{2}$ of $emf 4 V$ and internal resistance $8 \Omega$ (as shown in the figure). The potential difference across points $X$ and $Y$ is............ $V$
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