Question

A cylindrical resistor has a length of 2 m and a diameter of 0.1 m. If I hook up a 12 V battery to the resistor and notice that the current flowing through the resistor is 3.2 A, what is the resistivity of the resistor? A. 4.12 x 103 ? m B. 1.15 x 103 ? m C. 6.10 x 102 ? m D. 1.47 x 102 m

Answer 1

D . 1.47 x 10⁻² Ω-m

Step-by-step explanation:

L = length of the cylindrical resistor = 2 m

d = diameter = 0.1 m

A = Area of cross-section of the resistor = (0.25)
`\pi` d² = (0.25) (3.14) (0.1)² = 0.785 x 10⁻² m²

V = battery Voltage = 12 volts

`i` = current flowing through the resistor = 3.2 A

R = resistance of the resistor

Resistance of the resistor is given as

`R = (V)/(i)`

`R = (12)/(3.2)`

R = 3.75 Ω

`\rho` = resistivity

Resistance is also given as

`R = ( \rho L)/(A)`

`3.75 = ( \rho (2))/((0.785* 10^(-2)))`

`\rho` = 1.47 x 10⁻² Ω-m