In the given potentiometer circuit arrangement, the balancing length ${AC}$ is measured to be $250$ ${cm}$. When the galvanometer connection is shifted from point $(1)$ to point $(2)$ in the given diagram, the balancing length becomes $400\, {cm}$. The ratio of the emf of two cells, $\frac{\varepsilon_{1}}{\varepsilon_{2}}$ is -
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In the given circuit, the current flowing through the resistance $20\ \Omega$ is $0.3 \mathrm{~A}$, while the ammeter reads $0.9 \mathrm{~A}$. The value of $\mathrm{R}_1$ is_____________ $\Omega$.
A potential difference of $5 \,V$ is applied across a conductor of length $10 \,cm$. If drift velocity of electrons is $2.5 \times 10^{-4} \,m / s$, then electron mobility will be ............ $m ^2 V ^{-1} s ^{-1}$
Masses of three wires of copper are in the ratio of $1 : 3 : 5$ and their lengths are in the ratio of $5:3:1.$ The ratio of their electrical resistances are
Two conductors have the same resistances at $0^{\circ} \mathrm{C}$ but their temperature coefficients of resistance are $\alpha_1$ and $\alpha_2$. The respective temperature coefficients for their series and parallel combinations are :
A current of $10\, A$ exists in a wire of crosssectional area of $5\, mm ^{2}$ with a drift velocity of $2 \times 10^{-3}\, ms ^{-1}$. The number of free electrons in each cubic meter of the wire is ..........