Question

A copper transmission cable 140 km long and 11.0 cm in diameter carries a current of 150 A . The resistivity of cooper is 1.72 × 10−8 Ω⋅m. Part A What is the potential drop across the cable?

Answer 1

Answer:

The potential drop across the cable is 38 volts.

Explanation:

Given that,

Length of the copper cable, l = 140 km

Diameter of the cable, d = 11 cm

Radius, r = 5.5 cm

We need to find the potential drop across the cable. It can be calculated using Ohm's law. It is given by :

$V=IR$

R is the resistance

We know that the resistance is given by :

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

Voltage becomes :

$V=\rho\dfrac{l\times I}{A}\\\\V=\dfrac{1.72\times 10^{-8}\times 150\times 140\times 10^3}{\pi (5.5\times 10^{-2})^2}\\\\V=38\ volt$

So, the potential drop across the cable is 38 volts. Hence, this is the required solution.

Answer 2

Answer:

Explanation:

Length, l = 140 km = 140,000 m

Diameter, d = 11 cm = 0.11 m

radius, r = 0.055 m

resistivity, ρ = 1.72 x 10^-8 ohm metre

current, i = 150 A

let V is the potential difference.

Let R is the resistance of the wire.

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

where, A is the area of crossection

A = 3.14 x r²

A = 3.14 x 0.055 x 0.055

A = 9.5 x 10^-3 m²

$R = \frac{1.72 \times 10^{-8}\times 140000}{9.5 \times 10^{-3}}$

R = 0.254 ohm

According to Ohm's law

V = i x R

V = 150 x 0.254

V = 38 V