A potentiometer has uniform potential gradient. The specific resistance of the material of the potentiometer wire is $10^{-7} \, ohm-meter$ and the current passing through it is $0.1\, ampere$; cross-section of the wire is $10^{-6}\, m^2$. The potential gradient along the potentiometer wire is
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Two metal wires of identical dimensions are connected in series. If $\sigma _1$ and $\sigma _2$ are the conductivities of the metal wires respectively, the effective conductivity of the combination is
In the circuit shown in the figure, the switch $S$ is initially open and the capacitor is initially uncharged. $ I_1, I_2$ and $I_3$ represent the current in the resistance $2\,\Omega , 4\,\Omega $ and $8\,\Omega$ respectively.
$A$ brass disc and a carbon disc of same radius are assembled alternatively to make a cylindrical conductor. The resistance of the cylinder is independent of the temperature. The ratio of thickness of the brass disc to that of the carbon disc is [$\alpha$ is temperature coefficient of resistance and Neglect linear expansion ]
A $200\,\Omega $ resistor has a certain color code. If one replaces the red color by green in the code, the new resistance will be .............. $\Omega$
In a potentiometer circuit a cell of $EMF$ $1.5\, {V}$ gives balance point at $36\, {cm}$ length of wire. If another cell of $EMF$ $2.5\, {V}$ replaces the first cell, then at what length of the wire, the balance point occurs ? (in $cm$)
In the given figure switches $S_{1}$ and $S_{2}$ are in open condition. The resistance across $a b$ when the switches $S_{1}$ and $S_{2}$ are closed is $...\,\Omega$
An electrical circuit consists of ten $100 \,\Omega$ resistors. Out of these $10$ resistors, a group of $n _1$ resistors are connected in parallel and another group of $n _2$ resistors are separately connected in parallel. These two groups are then connected in series and this combination is connected to a voltage source of $100 \,V$. If the net current though the circuit is $2.5 \,A$. The values of $n _1$ and $n _2$ are