At 0º C, resistance of a conductor B is k times the resistance of conductor A. Temperature coefficients of resistance of conductors A and B at 0ºC are respectively, α A and α B . Find the temperature coefficient of resistance of series combination of A and B.
Text Solution
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Sol. Step 1: Define Resistance at Temperature T
The resistance of a conductor at temperature 
is given by the formula 
, where 
is the resistance at 
and 
is the temperature coefficient at 
.
For conductor A: 
For conductor B: 
Step 2: Calculate Total Series Resistance at T
The total resistance of the series combination at temperature 
, is the sum of the individual resistances:
Substituting the expressions from Step 1:
Factoring out 
and rearranging terms:
Step 3: Determine the Combined Temperature Coefficient
The total resistance can also be expressed in the standard form using the combined temperature coefficient 
and the total resistance at 
, 
:
We equate the expression from Step 2 to this standard form:
Dividing both sides by 
:
By comparing the coefficients of 
, we find the series temperature coefficient:
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