A metal wire of specific resistance $64 \times {10^{ - 6}}\,ohm - cm$ and length $198\, cm$ has a resistance of $7\, ohm$, the radius of the wire will be ............. $cm$
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Twelve wires each having resistance $2 \Omega$ are joined to form a cube. A battery of $6 \mathrm{~V}$ emf is joined across point $\mathrm{a}$ and $\mathrm{c}$. The voltage difference between $e$ and $f$ is.______.V.
A potentiometer has uniform potential gradient across it. Two cells connected in series $(i)$ to support each other and $(ii)$ to oppose each other are balanced over $6\,m$ and $2\,m$ respectively on the potentiometer wire. The $e.m.f.$’s of the cells are in the ratio of
Resistances ${R_1}$ and ${R_2}$ are joined in parallel and a current is passed so that the amount of heat liberated is ${H_1}$ and ${H_2}$ respectively. The ratio $\frac{{{H_1}}}{{{H_2}}}$ has the value
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