Question

A 24-gauge copper wire has a radius of 0.11 mm and is used to connect a speaker to an amplifier. The speaker is located 20 m away from the amplifier. What is the minimum resistance of the connecting speaker wires at 20 ˚C?

Answer 1

Resistance = 181.8 ohms

Step-by-step explanation:

R = L/r

R = 20/0.11

R = 181.8 ohms

Answer 2

Given Information:

Radius of copper wire = r = 0.11 mm = 0.11×10⁻³ m

Length of copper wire = L = 20 m

Required Information:

Resistance of the copper wire = R = ?

Answer:

Resistance of the copper wire = R = 18.1 Ω

Explanation:

The resistance of the copper wire is given by

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

Where ρ is the resistivity of the copper wire and is equal to 1.72×10⁻⁸ Ω/m at 20 ˚C, L is the length of the wire and A is the area of the wire and is given by

`A = \pi r^(2)`

Since the wire is used to connect speaker to the amplifier, two wires would be needed and the length of the wire becomes

`L = 2* 20 = 40\: m`

Finally, the resistance of the wire is

`R = \rho (L)/(\pi r^(2))\\\\R = 1.72*10^(-8)\cdot (40)/(\pi (0.11*10^(-3))^(2))\\\\R = 1.72*10^(-8)\cdot 1.052*10^(9)\\\\R = 18.1 \: \Omega`

Therefore, the minimum resistance of the connecting wires is 18.1 Ω