Two conductors have the same resistances at 0∘C but their temperature coefficients of resistance are α1 and α2. The respective temperature coefficients for their series and parallel combinations are :
Question
Two conductors have the same resistances at 0∘C but their temperature coefficients of resistance are α1 and α2. The respective temperature coefficients for their series and parallel combinations are :
Solution
The temperature coefficient of resistance for a series combination of resistors is not a straightforward calculation like the resistance itself. The same applies for a parallel combination of resistors. The overall temperature coefficient of resistance for a combination of resistors depends on the individual temperature coefficients and resistances of each resistor, and cannot be expressed as a simple function of the individual coefficients.
In other words, there is no direct formula to calculate the temperature coefficients for their series and parallel combinations based on α1 and α2. It would depend on the specific resistances of the two conductors and how much they change with temperature.
However, if the two conductors have the same resistance and the same temperature coefficient of resistance, then the temperature coefficient of resistance for their series and parallel combinations would also be the same as that of the individual conductors.
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