Question

(a) The resistance of a wire of 0.01 cm radius and 1.0 cm length is \( 7 \, \Omega \).
Calculate its resistivity.
OR
(b) An electric heater is rated 220 V; 11 A. Calculate the power consumed if the heater is operated at 200 V.

Hint:

(a) Resistivity formula: \( \rho = \frac{R \times A}{l} \). Remember to convert units to meters. (b) For constant resistance, power \( \propto V^2 \). \( P_2 = P_1 \times \left( \frac{V_2}{V_1} \right)^2 \).

Answer 1

(a) Calculation of Resistivity:

Given:
Radius (r) = 0.01 cm = 1 × 10⁻⁴ m
Length (L) = 1.0 cm = 1 × 10⁻² m
Resistance (R) = 7 Ω

Formula for resistivity:

R = ρL / A

Therefore,

ρ = RA / L

Cross-sectional area (A) = πr²

A = π (1 × 10⁻⁴)²
A = π × 1 × 10⁻⁸
A ≈ 3.14 × 10⁻⁸ m²

Now,

ρ = (7 × 3.14 × 10⁻⁸) / (1 × 10⁻²)

ρ = 21.98 × 10⁻⁸ / 10⁻²

ρ = 2.198 × 10⁻⁵ Ω m

Resistivity ≈ 2.2 × 10⁻⁵ Ω m

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(b) Calculation of Power Consumed at 200 V:

Given:
Rated voltage (V₁) = 220 V
Rated current (I₁) = 11 A

First find resistance of heater:

R = V₁ / I₁ = 220 / 11 = 20 Ω

Now when operated at 200 V:

Power formula:

P = V² / R

P = (200)² / 20

P = 40000 / 20

P = 2000 W

Power consumed = 2000 W