Pure copper wire of diameter = 2.0 mm has an electrical resistance, R, of 0.005 ohm/m (upside down U/m). p = 8900 kg/ m cubed, Cp= 440 J/(kg K). Passage of electrical current produces thermal energy generation = I triangle V= I squared R (J/sec).
Note that Units: Volts = J/coulomb; ohms = volts/amps; amps = coulombs/sec.
Calculate the thermal energy generation (J/sec) due to a steady current of 15 amps through a one meter length of wire.
To calculate the thermal energy generation (J/sec) due to a steady current of 15 amps through a one meter length of wire, we can use the formula I^2 * R, where I is the current and R is the electrical resistance.
Given:
Diameter of copper wire (d) = 2.0 mm = 0.002 m (converted to meters)
Electric resistance of copper wire (R) = 0.005 ohm/m
Current (I) = 15 amps
Length of wire (L) = 1 meter
First, we need to calculate the cross-sectional area (A) of the wire using the diameter:
A = π * (d/2)^2
A = 3.14 * (0.002/2)^2
A ≈ 3.14 * (0.001)^2
A ≈ 3.14 * 0.001^2
A ≈ 3.14 * 0.000001
A ≈ 0.00000314 m^2
Next, we can calculate the resistance (R) of the wire using the provided resistance per meter:
Resistance (R) = R * L
R = 0.005 ohm/m * 1 meter
R = 0.005 ohms
Now we can substitute the values into the formula I^2 * R to find the thermal energy generation:
Thermal energy generation = I^2 * R
Thermal energy generation = (15 amps)^2 * 0.005 ohms
Thermal energy generation = 225 * 0.005 J/sec
Thermal energy generation = 1.125 J/sec
Therefore, the thermal energy generation when 15 amps of current flows through a one meter length of the wire is 1.125 J/sec.