Question

(a) Write down an expression for the resistance of a metallic wire in terms of the resistivity.
(b) What will be the resistance of a metal wire of length 2 metres and area of cross-section 1.55 × 10−6 m2 if the resistivity of the metal be 2.8 × 10−8 Ω m?

Answer 1

Answer:

(a). R=pl/A

p= resistivity

(b) R= 2.8×10-8×2/1.55×20-6

=2.8×2×10^6/1.55×20^8

=5.6/1.55×10^2

=3.61×10^-2 ohm

Answer 2

Explanation:

(a) The ratio between the cross sectional area and length of the conductor is called as resistance (R) where as the ratio between the product of the resistance and its area to the length of the conductor is called as resistivity(ρ).

So, for a metallic wire, let the cross sectional area be A and length be l.

Resistance of the metallic wire be R and resistivity be ρ.

Then,$R=\frac{\rho l}{A}$ .

(b) According to the question, length of the metal wire, $l= 2 m$.

Area of cross-section, $A=1.55 \times 10^{-6} \mathrm{m}^{2}$.

Resistivity, $\rho=2.8 \times 10^{-8} \Omega$

From above, $R=\frac{\rho l}{A}=\frac{2.8 \times 10^{-8} \Omega \times 2 \mathrm{m}}{1.55 \times 10^{-6} \mathrm{m}^{2}}=0.036 \Omega$

Therefore, the resistance of the metal wire is 0.036 ohm.