Question

A rod of 2.0-m length and a square (2.0 mm × 2.0 mm) cross section is made of a material with a resistivity of 6.0 × 10–8 Ω ⋅ m. If a potential difference of 0.50 V is placed across the ends of the rod, at what rate is heat generated in the rod?

Answer 1

Answer:

= 8.33 Watt

Explanation:

$R = \frac{pl}{A}$

where,

p = resistivity

l = length

A = cross section area

Given that ,

p = resistivity = 6.0 × 10–8 Ω

l = 2m

A = cross section area = 2.0 mm × 2.0 mm = 4 x 10^-6 m^2

A = 2 x 2 mm^2 = 4 x 10^-6 m^2

p = 6 x 10^-8 ohm metre,

V = 0.5 V

Let R be the resistance of the rod

$R = p\frac{l}{A} \\\\R = 6.0 \times 10^-^8 (\frac{2}{4 \times 10^-^6} )\\\\R = 3 \times 10^-^2$

R = 3 × 10⁻²Ω

Heat generated  = V^2 / R

= (0.5)^2 / (3 x 10^-2)

 = 8.33 Watt