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Two conductors have the same resistance at `0^@C` but their temperature coefficient of resistanc are `alpha_1 and alpha_2`. The respective temperature coefficients of their series and parallel combinations are nearly
A. `(alpha_1+alpha_2)/2, alpha_1 + alpha_2`
B. `alpha_1+alpha_2, (alpha_1+alpha_2)/2`
C. `alpha_1+alpha_2, (alpha_1alpha_2)/(alpha_1+alpha_2)`
D. `(alpha_1+alpha_2)/2, (alpha_1+alpha_2)/2`

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Correct Answer - D
(d) `R_1 = R_0 [1+alpha_1Deltat], R_2 = R_0 [1+ alpha_2Deltat]`
In series, `R = R_1+R_2`
`= R_(0)[2+(alpha_1+alpha_2)Deltat] = 2R_0[1+ (alpha_1+alpha_2)/2 Deltat]`
`:. alpha_(eq) = (alpha_1+alpha_2)/2`
In parallel, `1/R = 1/R_1 + 1/R_2 = 1/(R_0[1+alpha_1Deltat]) + 1/(R_0[1+alpha_2Deltat]`
`rArr 1/(R_0/2(1+alpha_(eq)Deltat)) = 1/(R_0(1+alpha_1Deltat)) + 1/(R_0(1+alpha_2Deltat))`
`2(1-alpha_(eq)Deltat)= (1-alpha_1Deltat)(1-alpha_2Deltat) :. alpha_(eq) = (alpha_1+alpha_2)/2`.

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