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

Step-by-step explanation:

Given that,

Area of cross section of the carbon rod,
`A=5.1\ mm^2=5.1* 10^(-6)\ m^2`

Potential difference, V = 12 V

Current,
`I=4.4* 10^(-3)\ A`

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

V = IR

`R=(V)/(I)\\\\R=(12)/(4.4* 10^(-3))\\\\R=2727.27\ \Omega`

(b) The resistivity of carbon is,
`\rho=3.5* 10^(-5)\ \Omega-m`

The formula of resistance is given by :

`R=\rho(L)/(A)\\\\L=(RA)/(\rho)\\\\L=(2727.27* 5.1* 10^(-6))/(3.5* 10^(-5))\\\\L=397.4\ m`

Hence, this is the required solution.