General Physics 2, Chapter 25 You\'ve welded together two wires of different siz

Question

General Physics 2, Chapter 25

You've welded together two wires of different sizes, as shown below (note: electrical code doesn't normally allow this sort of thing: the current the thicker wire can cany safely could melt the smaller wire, causing a fire). Both lengths are 1.0 m long. Wire C is 1.00 mm in diameter and nas a resistivity of 2.0 Times 10-6 Ohmm. Wire D is 0.50 mm in diameter and has a resistivity of 1.0 Times 10-6 Ohmm. If you run 2 A of current through them, (a) what is the potential difference and the rate energy is dissipated between points 1 & 2? (b) How bout points 2 & 3?

Explanation / Answer

given,

length of the wires = 1 m

diameter of wire C = 1 mm

diameter of wire D = 0.5 mm

resistivity of wire C = 2 * 10^-6 ohm m

resistivity of wire D = 1 * 10^-6 ohm m

resistance = resistivity * length / area

resistance of wire C = 2 * 10^-6 * 1 / (pi * (0.5 * 10^-3)^2)

resistance of wire C = 2.546 ohm

resistance of wire D = 1 * 10^-6 * 1 / (pi * (0.25 * 10^-3)^2)

resistance of wire D = 5.093 ohm

by ohm's law

V = IR

V_c = 2 * 2.546

V_c = 5.092 ohm

potential difference between point 1 and 2 = 5.092 ohm

V_d = 2 * 5.093

v_d = 10.186 ohm

potential difference between point 2 and 3 = 10.186 ohm

power = V * I

power_c = 5.092 * 2

power_c = 10.184 W

rate of energy dissipated between points 1 and 2 = 10.184 W

power_d = 10.186 * 2

power_d = 20.372 W

rate of energy dissipated between point 2 and 3 = 20.372 W

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