Question
In a power station, a copper bar designed to carry many amperes of current is 2 m long and 10 cm2 in cross-section. Determine the resistance of the bar at 0 °C. What potential difference is needed to cause a current of 5000 A through the bar? The resistivity of copper at 0°C is 1.59 x 10–8 Ω m. Also compute the resistance of the bar if it is stretched to form a long and uniform wire of 1 mm2 cross-section.
Solution
Length of the copper bar, l = 2m
Area of cross-section of the bar, A=10 cm2 = 10 = 103 m2
Current across the bar, I = 5000 A
Resistivity of Copper at 0o C, 1.59 x 10–8 Ω m
The resistance of the bar is given by,
Now, using Ohm's law, the potential difference across its ends is
Volume of the bar = A.l = 2 x 10–3 m3
If the bar is stretched to form a long and uniform wire then,
Area of cross-section of the wire = 1 mm2 = 10–6 m2
Length of wire, l
The wire has the same amount of copper as the bar, but it is 2000 m long.
Therefore, the resistance of the wire is
Area of cross-section of the bar, A=10 cm2 = 10 = 103 m2
Current across the bar, I = 5000 A
Resistivity of Copper at 0o C, 1.59 x 10–8 Ω m
The resistance of the bar is given by,
Now, using Ohm's law, the potential difference across its ends is
Volume of the bar = A.l = 2 x 10–3 m3
If the bar is stretched to form a long and uniform wire then,
Area of cross-section of the wire = 1 mm2 = 10–6 m2
Length of wire, l
The wire has the same amount of copper as the bar, but it is 2000 m long.
Therefore, the resistance of the wire is
