The field coil of a machine is wound with 700 turns of copper wire of cross sectional area 0,375mm^2 .The mean length per turn is 400mm and thr resistivity of copper is 16×10^-3 micro ohm at 0 degrees Celsius. Determine the resistance of the coil at temperature of 60 degrees Celsius if the temperature coefficient of resistance referred to at 0 degrees Celsius, is 0,00426per degrees Celsius.
To determine the resistance of the coil at 60 degrees Celsius, we can follow these steps:
Step 1: Calculate the resistance at 0 degrees Celsius:
Given:
Number of turns (N) = 700
Cross-sectional area of wire (A) = 0.375 mm^2 = 0.375 × 10^-6 m^2 (converting mm^2 to m^2)
Mean length per turn (L) = 400 mm = 0.4 m (converting mm to m)
Resistivity of copper (ρ) = 16 × 10^-3 micro ohm = 16 × 10^-9 ohm m (converting micro ohm to ohm m)
The resistance (R) of a wire can be calculated using the formula:
R = (ρ * L) / A
Substituting the given values:
R at 0 degrees Celsius = (16 × 10^-9) * (0.4) / (0.375 × 10^-6) = 17.067 ohms (rounded to three decimal places)
Step 2: Calculate the change in resistance due to temperature:
Given:
Temperature coefficient of resistance (α) = 0.00426 per degree Celsius
Change in temperature (ΔT) = 60 - 0 = 60 degrees Celsius (since we want to find the resistance at 60 degrees Celsius)
The change in resistance (ΔR) can be calculated using the formula:
ΔR = R * α * ΔT
Substituting the given values:
ΔR = 17.067 * 0.00426 * 60 = 4.129 ohms (rounded to three decimal places)
Step 3: Calculate the resistance at 60 degrees Celsius:
The resistance at 60 degrees Celsius (R at 60 degrees Celsius) can be calculated using the formula:
R at 60 degrees Celsius = R at 0 degrees Celsius + ΔR
Substituting the calculated values:
R at 60 degrees Celsius = 17.067 + 4.129 = 21.196 ohms (rounded to three decimal places)
Therefore, the resistance of the coil at a temperature of 60 degrees Celsius is approximately 21.196 ohms.