1.

A resistance R of therimal coefficient of resistivity `alpha` is connected in parallel with a resistance 3R. Having thermal coeffiecinet of resistivity `2alpha` Find the value of `alpha_(eff)`

Answer» The equivalent resistance at `0^@C` is
`R_0 = (R_(10)R_(20))/(R_(10) + R_(20))` …(i)
The equivalent resistance at `t^@`C is
`R = (R_1R_2)/(R_1+R_2)` .....(ii)
But `R_1 = R_(10)(1 + alphat)` .....(iii)
`R_2 = R_(20) (1+2 alphat)` ....(iv)
and `R = R_0 (1+alpha_(eft) t)` ...(v)
Putteing the value of (i), (iii), (iv) and (v) in Eq. (ii), we have
`alpha_(eff) = (5)/(4)alpha`


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