Given Information:
Diameter of the wire = d = 0.51 mm
Length of the wire = L = 8.5 m
Resistance of the speaker = Rsp = 8 Ω
Required Information:
Part A: Resistance of the connecting wire = R = ?
Part B: Ratio of the resistance of connecting wire and speaker = ?
Answer:
Part A: R = 1.43 Ω
Part B: R is 17.8% of Rsp
Explanation:
R = ρL/A
where ρ is the resistivity of the copper wire 1.72x10⁻⁸ Ω/m (at 20 ˚C)
A is the area of the copper wire A = πr²
r = d/2 = 0.51/2 = 0.255 = 0.0255 cm 0.000255 m
Part A: What is the minimum resistance of the connecting speaker wires at 20 ˚C?
R = ρL/πr
R = 1.72x10⁻⁸(8.5)/π*(0.000255)²
R = 0.715 Ω
Since two connecting wires are needed so total resistance becomes
R = 2*715 = 1.43 Ω
Part B: Compare the resistance of the wire to the resistance of the speaker (RSP = 8 Ω)
Resistance of connecting wires = 1.43 Ω
Resistance of the speaker = 8 Ω
1.43/8 = 0.178 = 17.8 %
Therefore, resistance of the connecting wires is 17.8% of the speaker resistance.
