A potentiometer wire of length L and a resistance r are connected in series with a battery of e.m.f. E₀ and a resistance r₁. An unknown e.m.f. E is balanced at a length $$l$$ of the potentiometer wire. The e.m.f. E will be given by

Across a metallic conductor of non-uniform cross section a constant potential difference is applied. The quantity which remains constant along the conductor is

A, B and C are voltmeters of resistance R, 1.5 R and 3R respectively as shown in the figure. When some potential difference is applied between X and Y, the voltmeter readings are V_A, V_B and V_C respectively, Then

A potentiometer wire has length 4 m and resistance 8 $$\Omega $$. The resistance that must be connected in series with the wire and an accumulator of e.m.f. 2 V, so as to get a potential gradient 1 mV per cm on the wire is