Question

Two pieces of 14-gauge wire (diameter=0.163cm) each are 50m in length. One wire is made of aluminum, the other of tungsten; both are maintained at a temperature of 20°C. The wires are joined together at one end to form a sign wire of 100m length. A potential difference of 12V is applied across the length of this compound wire. (a) What is the resistance of each 50m segment? (b) What is the current in each? (c) What is the potential difference across each segment? (d) What is the electric field in each segment?

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Aluminum(2.810 Tungsten(5.610-8)

Answer 1

Resistivity of aluminium 2.82*10^-8 ohm-m

Resistivity of tungsten is 5.6*10^-8 ohm-m

a)

Area

A=pi*D²/4 =pi*(0.163*10^-2)²/4 =2.0867*10^-6 m²

Resistance of each wire

R_Al=p_ALL/A =(2.82*10^-8)(50)/(2.0867*10^-6)

R_Al=0.6757 ohms

R_Tu =p_TuL/A =(5.6*10^-8)(50)/(2.0867*10^-6)=1.3418 ohms

b)

equivalent resistance

R=0.6757+1.3418 =2.0175 ohms

Current flowing through each wire

I_Al=I_Tu=12/2.0175 =5.948 A

c)

V_AL=5.948*0.6757=4.02 V

V_Tu=5.948*1.3418=7.98 V

d)

E_Al=4.02/50 =0.0804 V/m

E_Tu=7.98/50 =0.1596 V/m