Question

Two coils connected in series has resistance of 600 ohm and 300ohm and temperature coefficients of 0.1% and 0.4% respectively. The resistance of the combination at 50°C will be

Answer 1

Resistance of 600 Ω resistor at 50°C is = 600 [1 + 0.001 (50 − 20)] = 618 Ω Similarly, resistance of 300 Ω resistor at 50°C is = 300 [1 + 0.004 (50 − 20)] = 336 Ω Hence, total resistance of combination at 50°C is = 618 + 336 = 954 Ω Let β = resistance-temperature coefficient at 20°C Now, combination resistance at 20°C = 900 Ω Combination resistance at 50°C = 954 Ω ∴ 954 = 900 [ 1 + β (50 − 20)] ∴ β = 0.002.

$Resistance of 600 Ω resistor at 50°C is = 600 [1 + 0.001 (50 − 20)] = 618 Ω  Similarly, resistance of 300 Ω resistor at 50°C is = 300 [1 + 0.004 (50 − 20)] = 336 Ω  Hence, total resistance of combination at 50°C is = 618 + 336 = 954 Ω  Let β = resistance-temperature coefficient at 20°C  Now, combination resistance at 20°C = 900 Ω  Combination resistance at 50°C = 954 Ω  ∴ 954 = 900 [ 1 + β (50 − 20)]  ∴ β = 0.002Read more on Sarthaks.com - https://www.sarthaks.com/457456/two-coils-connected-in-series-have-resistances-of-600-and-300-with-tempt-coeff-of-0-1$

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