A conductor of length L and resistance R is cut into two equal halves. These two halves are then connected in parallel. Find the equivalent resistance of this parallel combination?

Correct option is A

The correct answer is: (a) R/4
Explanation:
· Original conductor: Length = L, Resistance = R.
· When cut into two equal halves, each piece has length L/2.
· Resistance of each half =$$\dfrac{R}{2} (since R∝L)$$​).
· Now, both halves are connected in parallel:
​$$\frac{1}{R_{eq}} = \frac{1}{R/2} + \frac{1}{R/2} = \frac{2}{R/2} = \frac{4}{R}$$​​
Information Booster:
· Resistance formula: $$R = \rho \dfrac{L}{A}$$​, where ρ\rhoρ = resistivity, L = length, A = cross-sectional area.
· Cutting a conductor reduces its resistance in proportion to length.
· In parallel combination: Equivalent resistance is less than the smallest individual resistance.
· In series combination: Equivalent resistance is the sum of all resistances.
· This principle is widely used in wire-wound resistors and circuit design.