A carbon resistor dissipates 60 W of power from 120 V source at 20 °C. How much power will be dissipated in the resistor at 120 °C if connected across the same source? Assume the temperature coefficient of carbon at 20 °C is - 0.0005 per °C.
Answers
Explanation:
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Given : A carbon resistor dissipates 60 W of power from 120 V source at 20 °C.
Assume the temperature coefficient of carbon at 20 °C is - 0.0005 per °C.
To Find : How much power will be dissipated in the resistor at 120 °C if connected across the same source?
Solution:
Power = Voltage * Current
60 = 120 * Current
=> Current = 0.5 A
Voltage = Current * Resistance
=> 120 = 0.5 * R
=> R = 240 Ω
RT = R₀(1 + αΔT)
ΔT = 120 - 20 = 100 °C
α = 0.0005 per °C.
R₁₂₀ = 240 ( 1 + 0.0005 * 120)
=> R₁₂₀ = 254.4 Ω
power will be dissipated = V²/R
= 120²/ 254.4
= 56.6 W
power will be dissipated in the resistor at 120 °C = 56.6 W
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