Question

Now let's consider the resistance of speaker wire. Suppose you're hooking up a pair of stereo speakers, You happen to have on hand some 20-m-Jong pieces of 16 gauge copper wire (diameter 1.3 mm); you use them to connect the speakers to the amplifier. These wires are longer than needed, but you just coil up the excess length instead of cutting them. What is the resistance of one of these wires? To improve the performance of the system, you purchase 3.0-m-long speaker cables that are made with 8 gauge copper wire (diameter 3.3 mm). What is the resistance of one of these cables? Shows our sketch. The resistivity of copper at room temperature is rho = 1.72 times 10^-8 Ohm. The cross-sectional area A of a wire is related to its radius by A = pi r^2. To find the resistances, we use R = (1.72 times 10^-8 Ohm middot m) (20 m)/pi (6.5 times 10^-4 m)^2 = 0.26 Ohm R = (1.72 times 10^-8 Ohm middot m) (3.0 m)/pi (1.65 times 10^-3 m)^2 = 6.0 times 10^-3 Ohm The shorter, fatter wires offer more than 40 times less resistance than the longer, skinnier ones. The lower the resistance, the higher the current flowing to the speakers. 14 gauge copper wire has a diameter of 1.6 mm. What length of this wire has a resistance of 1.4 Ohm? Express your answer in meters to two significant figures.

Answer 1

Resistance (R) = rho l/A l = AR/rho = pi (0.8 times 10^-3)^2 times 1.4/1.72 times 10^-8 l = 163.65 m = 160 m