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$n$ identical cells each of $e.m.f.$ $E$ and internal resistance $r$ are connected in series. An external resistance $R$ is connected in series to this combination. The current through $R$ is
There are $n$ similar conductors each of resistance $R$. The resultant resistance comes out to be $x$ when connected in parallel. If they are connected in series, the resistance comes out to be
In a potentiometer experiment shown here, for the position $X$ of the jockey $J,$ there occurs a null deflection in the galvanometer. Then the potential difference between points $A$ and $X$ is ................ $V$
In the given figure $R_1=10 \Omega, R_2=8 \Omega, R_3=4 \Omega$ and $R_4=8 \Omega$. Battery is ideal with emf $12 \mathrm{~V}$. Equivalent resistant of the circuit and current supplied by battery are respectively.
The resistance of a wire is $5\,ohm$ at $50\,^o C$ and $6\,ohm $ at $100\,^o C$. The resistance of the wire at $0\,^o C$ will be .............. $\Omega$
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 :