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Two equal resistance at `0^(@)C` with temperature coefficient of resistance `alpha_(1)` and `alpha_(2)` joined in series act as a single resistance in a circuit the temperature coefficient of their single resistance will beA. `alpha_(1)+alpha_(2)`B. `(alpha_(1)alpha_(2))/(alpha_(1)+alpha_(2))`C. `(alpha_(1)-alpha_(2))/(2)`D. `(alpha_(1)+alpha_(2))/(2)` |
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Answer» Correct Answer - 4 At `o^(@)C`, let two resistance be `R_(0)` and `R_(0)`. At `t^(@)C` let the resistances be `R_(1)` and `R_(2)`. `therefore R_(1)=R_(0)(1+alpha_(1)t)` `R_( 2)=R_(0)(1+alpha_(2)t)` when combined is series. Temperature coefficient `(beta)=("change in resistance")/("Original resistance"xxt)` or `beta=("Final resistance"-"Original resistance")/("Original resistance"xxt)` `beta=((R_(1)+R_(2))-2R_(0))/((2R_(0))t)` `=R_(0)(1+alpha_(1)t)+R_(0)(1+alpha_(2)t)(-2)/(2R_(0)xxt)` `=(2+alpha_(1)t+alpha_(2)t-2)/(2t)=(alpha_(1)+alpha_(2))/(2)` |
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