A potential difference of 250v is applied to a field winding at 15°C and the current is 5A.?
What will be the mean temperature of the winding when the current has fallen to 3.91A, with the applied voltage being constant. Assume α15=1/254.5 per degree Celsius. (α15: Resistance temperature coefficient at 15°C).
1. 18.45°C
2. 86.25°C
3. 100°C
4. 75°C
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Verified answer
Given V=250V, To=15°C, I(To)=5.0A, I(T)=3.91A, α(To)=1/254.5 1/°C
R(15) = V/I(15) = 50Ω
R(T) = V/I(T) = 63.9Ω
Resistance varies with temp. coefficient as:
R(T) = R(To)(1+αΔT)
Which can be rewritten as:
ΔT = ((R(T)/R(To))-1)/α
ΔT = ((63.9/50)-1)/(1/254.5) = 70.7°C
So final mean temp is given by:
T = To+ΔT = 85.7°C