Question

A rod of 2.0-m length and a square (2.0 mm x 2.0 mm) cross section is made of a material with a resistivity of 6.0 x 10^-8 0.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:

Heat generated in the rod is 8.33 watts.

Explanation:

It is given that,

Length of rod, l = 2 m

Area of cross section, $A=2\ mm\times 2\ mm=4\ mm^2=4\times 10^{-6}\ m^2$

Resistivity of rod, $\rho=6\times 10^{-8}\ \Omega-m$

Potential difference, V = 0.5 V

The value of resistance is given by :

$R=\rho\dfrac{l}{A}$

$R=6\times 10^{-8}\ \Omega-m\times \dfrac{2\ m}{4\times 10^{-6}\ m^2}$

R = 0.03 ohms

Let H is the rate at which heat is generated in the rod . It is given by :

$\dfrac{H}{t}=I^2R$

Since, $I=\dfrac{V}{R}$

$\dfrac{H}{t}=\dfrac{V^2}{R}$

$\dfrac{H}{t}=\dfrac{(0.5)^2}{0.03}$

$\dfrac{H}{t}=8.33\ watts$

So, the at which heat is generated in the rod is 8.33 watts. Hence, this is the required solution.