A resistance of $4\,\Omega $ and a wire of length $5\,m$ and resistance $5\,\Omega $ are joined in series and connected to a cell of $e.m.f.$ $10\, V$ and internal resistance $1\,\Omega $. A parallel combination of two identical cells is balanced across $300\, cm$ of the wire. The $e.m.f.$ $E$ of each cell is ........... $V$
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When a current of $2\, A$ flows in a battery from negative to positive terminal, the potential difference across it is $12\, V$. If a current of $3\, A$ flows in the opposite direction potential difference across the terminals of the battery is $15\, V$, the $emf$ of the battery is ............... $\mathrm{V}$
The current density in a cylindrical wire of radius $4 \; mm$ is $4 \times 10^{6} \; Am ^{-2}$. The current through the outer portion of the wire between radial distance $\frac{R}{2}$ and $R$ is $\dots \; \pi A .$
The resistance of a wire of uniform diameter $d$ and length $L$ is $R$. The resistance of another wire of the same material but diameter $2d$ and length $4L$ will be
The current density is a solid cylindrical wire of radius $R ,$ as a function of radial distance $r$ is given by $J ( r )= J _{0}\left(1-\frac{ r }{ R }\right) .$ The total current in the radial region $r =0$ to $r =\frac{ R }{4}$ will be
A resistor develops $300 \,J$ of thermal energy in $15 \,s$, when a current of $2\, A$ is passed through it. If the current increases to $3 \,A$, the energy developed in $10\,\,s$ is........$J.$
In the circuit shown, the reading of the ammeter (ideal) is the same with both switches open as with both closed find the value of resistance $R$ in $ohm$ . ................ $\Omega$