Question

A resistor is constructed of a carbon rod that has a uniform cross-sectional area of 5.10 mm2. When a potential difference of 12.0 V is applied across the ends of the rod, the rod carries a current of 4.40 ✕ 10-3 A.(a)What is the resistance of the rod?
(b) What is the rod’s length?

Answer 1

Explanation:

Given that,

Area of cross section of the carbon rod, $A=5.1\ mm^2=5.1\times 10^{-6}\ m^2$

Potential difference, V = 12 V

Current, $I=4.4\times 10^{-3}\ A$

(a) Let R is the resistance of the rod. Using Ohm's law to find it as :

V = IR

$R=\dfrac{V}{I}\\\\R=\dfrac{12}{4.4\times 10^{-3}}\\\\R=2727.27\ \Omega$

(b) The resistivity of carbon is,   $\rho=3.5\times 10^{-5}\ \Omega-m$

The formula of resistance is given by :

$R=\rho\dfrac{L}{A}\\\\L=\dfrac{RA}{\rho}\\\\L=\dfrac{2727.27\times 5.1\times 10^{-6}}{3.5\times 10^{-5}}\\\\L=397.4\ m$

Hence, this is the required solution.