Problem 2 (20 pointsy You need to use the floodlight in a shed that is not wired

Question

Problem 2 (20 pointsy You need to use the floodlight in a shed that is not wired for electricity, so you connect it to a 500m extension cord and plug it into a 120V outlet in the nearest building. The cord is made of copper and each wire inside the cord has a diameter of 1.5 mm. The resistivity of copper is 1.69 x 10 Q.m. a) Calculate the resistance that the cord adds to the circuit. b) If the resistance of the floodlight is 50 what is the resistance of the whole circuit including the bulb and cord? c) How much current flows through the whole circuit? d) What is the voltage drop across the bulb?

Explanation / Answer

Given

length of wire l = 500m

voltage v = 120 V

radius r = 1.5 /2 = 0.75 * 10^-3 m

area of cross section A = pi*r^2 = 3.14 * sqr(0.75 * 10^-3)

A = 1.76 * 10^-6 m^2

resistivity of copper is 1.69 * 10^-8

a) resistance R = rho * L /A

R = 1.69 * 10^-8 * 500 / 1.76 * 10^-6 m^2

R = 19.2 micro ohm

b) total resistance is 19.2 + 50 = 69.2 ohm

c) current i = v/total resistance

i = 120/69.2

i= 1.73 A

d) voltage drop across the bulb is Vb = i* 50

Vb = 1.73*50

Vb = 86.7 V

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