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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 nearlyA. `alpha_(1)+ alpha_(2) (alpha_(1)+ alpha_(2))/(2)`B. `alpha_(1)+ alpha_(2) (alpha_(1)alpha_(2))/(alpha_(1)+ alpha_(2))`C. `(alpha_(1)+ alpha_(2))/(2), (alpha_(1)+ alpha_(2))/(2)`D. `(alpha_(1)+ alpha_(2))/(2), alpha_(1)+ alpha_(2)` |
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Answer» Correct Answer - c Let `R_(t_1),R_(t_2)` be the resistance of two combination at temperature `t_(1)^(@)C` temperature Then, `R_(1) =R_(0)(1 + alpha_(1)t)` and `R_(2) =R_(0)(1 + alpha_(1)t)` When conduction are in series let `alpha_(S)` be the effective temperature coeffecient of resistances series Then effective resistance at temperature `t^(@)C` is `R_(1) = R_(t_1) +R_(t_2)` `2R_(0) (1 + alpha_(S)t)= R_(0)(1+ alpha_(1)t) +(1+ R_(0)(1 + alpha_(2)t)` or `2 + 2alpha_(1)t = (1+alpha_(1)t ) +(1+alpha_(2)t)` `= 2 +(alpha_(1)+alpha_(2))t` On solving `alpha_(s) = (alpha_(1) +alpha_(2))/(2)` When conductors are in parallel of resistance in parallel. Then `(1)/(R_(P)) = (1)/(R_(t_1)) + (1)/(R_(t_2))` or `(1)/((R_(0)//2)+[1+alpha_(p)t)) = (1)/(R_(0)(1+alpha_(1)t)) +(1)/(R_(0)(1+alpha_(2)t))` or `(2)/((1+alpha_(P)t)) = (1)/((1+alpha_(1)t)) + (1)/((1+alpha_(2)t))` or `2(1+alpha_(p)t)^(-1)=(1+alpha_(1)t)^(-1)+(1+alpha_(2)t)^(-1)` or `2(1 - alpha_(p)t)0 = ( 1- alpha_(1)t) +(1 - alpha_(2)t)` On solving `alpha_(p) = (alpha_(1) + alpha_(2))/(2)` |
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