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A wire 50 cm long and 1 mm² in cross-section carries a current of 4 A when connected to a 2 V battery. The resistivity of the wire is

Asked in CBSE AIPMT 1994 · Ohm's law and resistivity

(1) 4×10⁻⁶ Ω m
(2) 1×10⁻⁶ Ω m
(3) 2×10⁻⁷ Ω m
(4) 5×10⁻⁷ Ω m

Answer: (2) 1×10⁻⁶ Ω m

Step-by-step solution

R = V/I = 2/4 = 0.5 Ω.

A = 1 mm² = 10⁻⁶ m², l = 0.5 m.

ρ = (RA)/l = (0.5×10⁻⁶)/(0.5)

ρ = 1×10⁻⁶ Ω m.

Why the other options are wrong

(1) Comes from inverting Ohm's law, R = I/V = 2 Ω, which gives 2×10⁻⁶/0.5.
(3) Would need R = 0.1 Ω; no single slip with these numbers reproduces it.
(4) This is RA = 0.5×10⁻⁶, with the division by the 0.5 m length left out.

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