$AB$ is a potentiometer wire of length $100\, cm$ and its resistance is $10 \,\Omega$. It is connected in series with a resistance $R = 40 \,\Omega$ and a battery of $e.m.f.$ $2 \,V$ and negligible internal resistance. If a source of unknown $e.m.f.$ $E$ is balanced by $40\, cm$ length of the potentiometer wire, the value of $E$ is ................. $V$
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Four identical electrical lamps are labelled $1.5\,V$, $0.5\,A$ which describes the condition necessary for them to operate at normal brightness. A $12\,V$ battery of negligible internal resistance is connected to lamps as shown, then
The current in the primary circuit of a potentiometer is $0.2\, A$. The specific resistance and cross section of the potentiometer wire are $4\times10^{-7}\,ohm$ $metre$ and $8\times10^{-7}\, m^2$ respectively. The potential gradient will be equal to .............. $V/m$
Coefficient of linear expansion of material of resistor is $\alpha$. Its temperature coefficient of resistivity and resistance are $\alpha_\rho$ and $\alpha_R$ respectively, then correct relation is
A current $I$ flows through a uniform wire of diameter $d,$ when the mean drift velocity is $v_d.$ The same current will flow through a wire of diameter $d/2$ made of the same material, if the mean drift velocity of the electrons is
We have two wires $A$ and $B$ of same mass and same material. The diameter of the wire $A$ is half of that $B$. If the resistance of wire $A$ is $24\, ohm$ then the resistance of wire $B$ will be ................ $Ohm$
A wire has a resistance of $12\, ohm$. It is bent in the form of equilateral triangle. The effective resistance between any two corners of the triangle is