Since you cannot afford expensive cable to hook up between your loudspeaker and music amplifier, you try some common 14-gauge diameter = 1.628 mm) copper wire. If the total length of the wire there and back) used for each speaker to amplifier hookup was 10 m, then calculate the resistance in the wire for one channel ρ_Cu = 1.7 × 10^-8 Ω/m).

Question

Quizplus · Accepted Answer

The resistance of the wire can be calculated using the formula:

R = (ρL)/A

where R is the resistance, ρ is the resistivity of copper (given as 1.7 × 10^-8 Ω/m), L is the length of the wire (10 m in this case), and A is the cross-sectional area of the wire.

The cross-sectional area of a 14-gauge wire is approximately 2.08 mm^2 (or 2.08 × 10^-6 m^2).

Plugging in the values, we get:

R = (1.7 × 10^-8 Ω/m × 10 m) / (2.08 × 10^-6 m^2) 
R = 8.2 × 10^-3 Ω

Since there are two channels (left and right) for the loudspeakers, we need to double the resistance to get the total resistance for both channels:

Total resistance = 2 × 8.2 × 10^-3 Ω = 1.64 × 10^-2 Ω

This corresponds to option D: 8.2 × 10^-2 Ω.

Since You Cannot Afford Expensive Cable to Hook Up Between