This question is meant to give you some practice calculating resistance, current

Question

This question is meant to give you some practice calculating resistance, current, voltage etc. Consider a wire made of two parts of the same diameter, 0.5 mm, but of different materials: One part is made of silver and 1 m long, the other is made of copper and 80 cm long. You can think of it as two resistors (non-ideal wires) in series. When you apply a potential difference of 6 V to the ends of the composite wire,

a) what is the resistance of each section?

b) What is the current in each section?

c) What is the magnitude of the electric field in each section?

d) What is the potential difference between the ends of the silver section of the wire?

Explanation / Answer

Cross - sectional area of the wire, A = pi*r^2 = 3.141*0.00025^2 = 1.963 x 10^-7 m^2

From the table, resistivity of silver = 1.59 x 10^-8 ohm.m

and, resistivity of copper = 1.68 x 10^-8 ohm.m

(a) Resistance of silver, Rs = k*l/A = (1.59x10^-8x1) / (1.963x10^-7) = 0.081 ohm

Resiatnce of copper section, Rc = (1.68x10^-8x0.80) / (1.963x10^-7) = 0.068 ohm

(b) The two sections are connected in series, so the total resistance R = Rs + Rc = 0.081 + 0.068 = 0.149 ohm

So, current in each section = 6 / 0.149 = 40.3 A

(c) Electric field in silver section = Vs / ls = (40.3x0.081) / 1 = 3.3 V/m

Electric field in copper section = Vc / Ic = (40.3x0.068) / 0.80 = 3.4 V/m

(d) Potential difference between the ends of silver section = 40.3x0.081 = 3.3 V

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