A uniform wire AB of resistance R₀ is connected across an ideal DC voltage source V₀ . A resistor R is connected between end A and a sliding contact C on the wire. Let x be the fractional distance of C from A (where x = AC / AB ). Based on this circuit, two statements are given below: Statement I: As the sliding contact moves from A to B, the potential difference across R increases monotonically. Statement II: If R R

Step-by-step solution

The resistance of segment AC is x R₀ and segment CB is (1-x) R₀ . The equivalent resistance of AC and R in parallel is R_p = R (x R₀) R + x R₀ . The total resistance of the circuit is R_ eq = R_p + (1-x) R₀ = R x R₀ R + x R₀ + (1-x) R₀ = R R₀ + x R₀^2 - x^2 R₀^2 R + x R₀ . The potential difference across R is V(x) = V₀ R_p R_ eq = V₀ R x R + x(1-x)R₀ . To check Statement I, we can write V₀ V(x) = 1 x + (1-x)R₀ R . As x increases from 0 to 1 , both 1 x and (1-x) strictly decrease, so V₀ V(x) decreases. This means V(