1. When a constant current is flowing through a wire having uniform area of cross section and uniform composition the potential difference across any length of the wire is directly proportional to its length.
V ∝ l.
2. The resistance of potentiometer
Rp = 4 × 3 = 12Ω
Current through the potentiometer
I = \(\frac{E}{R+R_p}=\frac{4}{20+12}\) = 0.125 A
Potential across potentiometer wire
VAB = IRp = 0.125 × 12 = 1.5V
Potential gradient k = \(\frac{V_{AB}}{I}=\frac{1.5}{3}\) = 0.5 V/m
Balancing length for cell E2 is given from equation
E2 = kI2 = 0.5I2
\(I_2=\frac{E}{k}=\frac{1}{0.5}\) = 2 m
3. If E2 > E1 , we will not get null deflection. The potential difference across the potentiometer wire AB should be higher than the emf of E2 .