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Physics · Electrical energy and power, electrical resistivity and conductivity

A wire long and in cross section carries a current of 4 A when connected to a 2

A wire \( 50 \mathrm{cm} \) long and \( 1 \mathrm{mm}^{2} \) in cross section carries a current of 4 A when connected to a 2 V battery. The resistivity of the wire is

  • A. \( 2 \times 10^{-7} \Omega m \)
  • B. \( 5 \times 10^{-7} \Omega m \)
  • C. \( 4 \times 10^{-6} \Omega m \)
  • D. \( 1 \times 10^{-6} \Omega m \)

Step-by-step solution

Given: L = 50 cm = 0.5 m, A = 1 mm² = 1×10⁻⁶ m², I = 4 A, V = 2 V. Using Ohm's law, R = V/I = 2/4 = 0.5 Ω. Using resistivity formula R = ρL/A, so ρ = RA/L = (0.5 × 1×10⁻⁶)/0.5 = 1×10⁻⁶ Ω m.
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