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A wire of length $10 \mathrm{~cm}$ and radius $\sqrt{7} \times 10^{-4} \mathrm{~m}$ connected across the right gap of a meter bridge. When a resistance of $4.5 \ \Omega$ is connected on the left gap by using a resistance box, the balance length is found to be at $60 \mathrm{~cm}$ from the left end. If the resistivity of the wire is $\mathrm{R} \times 10^{-7} \Omega \mathrm{m}$, then value of $\mathrm{R}$ is :
Consider the ladder network shown in figure. What should be the value of resistance $R$, so that effective resistance between $A$ and $B$ becomes independent of number of elements in the combination is ............. $\Omega$
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 cell of negligible resistance and $e.m.f.$ $2$ $volts$ is connected to series combination of $2$, $3$ and $5\, ohm$. The potential difference in volts between the terminals of $3\, ohm$ resistance will be
The four arms of a Wheatstone bridge have resistances as shown in the figure. A galvanometer of $15\, \Omega$ resistance is connected across $BD$. Calculate the current through the galvanometer when a potential difference of $10\, V$ is maintained across $AC.$
The potential gradient along the length of a uniform wire is $10\,volt/metre$. $B$ and $C$ are the two points at $30\,cm$ and $60\,cm$ point on a meter scale fitted along the wire. The potential difference between $B$ and $C$ will be ............. $volt$