Two conductors have the same resistances at 0 C but their temperature coefficients of resistance are 1 and 2. The respective temperature coefficients for their series and parallel combinations are :
- 1+ 2, 1 2 1+ 2
- 1+ 22, 1+ 22
- 1+ 2, 1+ 22
- 1+ 22, 1+ 2
Answer
(2) 1+ 22, 1+ 22
Solution
At t C: R1=R0(1+ 1t), R2=R0(1+ 2t)
Series: Rs=R1+R2=2R0 [1+ 1+ 22t ]
s= 1+ 22
Parallel: Rp= R1R2R1+R2= R0(1+ 1t)(1+ 2t)2+( 1+ 2)t
R02 [1+( 1+ 2)t ] [1- 1+ 22t ] ( t 1, drop t2 terms)
R02 [1+ 1+ 22t ] p= 1+ 22
Answer: (2)