A "Bus" bar is in the form of a slab of copper 2meters long, 1cm wide, and 10 cm thick.
a) What is the resistance of the bar at 0 degrees celcius?
b) What potential difference is needed to push 5000 amps through the bar?
Look up the resistivity of copper. Call it r. For pure copper,
r = 1.67*10^-7 ohm-cm
(a) Multiply "r" by the bar's length (200 cm) and divide by the cross sectional area (10 cm^2), to get the resistance in ohms, R.
(b) V = I * R (volts)
I = 5000 A
Solve for V
To solve these problems, we need to use the formula for electrical resistance and Ohm's Law.
a) To find the resistance of the bar at 0 degrees Celsius, we need to know the resistivity of copper at that temperature. The resistivity (ρ) of copper changes with temperature. The formula for calculating the resistance (R) of a conductor is:
R = (ρ * L) / A
where
R = resistance
ρ = resistivity
L = length of the conductor
A = cross-sectional area of the conductor
First, we need to determine the resistivity of copper at 0 degrees Celsius. The resistivity of copper at 20 degrees Celsius is approximately 1.7 x 10^-8 ohm-meters. To calculate the resistivity at 0 degrees Celsius, we need to consider the temperature coefficient of resistivity for copper (αcopper), which is approximately 0.0039 per degree Celsius.
Resistivity at 0 degrees Celsius (ρ0) = ρ20 * (1 + αcopper * (0 - 20))
ρ0 = 1.7 x 10^-8 * (1 + 0.0039 * (0 - 20))
ρ0 = 1.7 x 10^-8 * (1 + 0.0039 * -20)
ρ0 = 1.7 x 10^-8 * (1 - 0.078)
ρ0 = 1.7 x 10^-8 * 0.922
ρ0 = 1.5684 x 10^-8 ohm-meters
Now we can substitute the values into the resistance formula:
R = (ρ0 * L) / A
R = (1.5684 x 10^-8 * 2) / (0.01 * 0.1)
R = 3.1368 x 10^-8 / 0.001
R = 3.1368 x 10^-5 ohms
Therefore, the resistance of the copper bar at 0 degrees Celsius is approximately 3.1368 x 10^-5 ohms.
b) To find the potential difference (V) required to push 5000 amps through the bar, we can use Ohm's Law. Ohm's Law states that V = I * R, where V is the potential difference, I is the current, and R is the resistance.
V = 5000 * 3.1368 x 10^-5
V = 156.84 volts
Therefore, a potential difference of approximately 156.84 volts is needed to push 5000 amps through the bar.