The resistance of rwo wires `A` and `B` at `20^@C` are `3 Omega` and `4 Omega` respectively. At what temperature will the resistance be equal ? `alpha_(A) = 6 xx 10^-3 K^(-1), alpha_(B) = 2 xx 10^-3 K^-1`. Neglect any thermal expansion.

Explanation

`A : R_theta = R_20[1 + alpha_(A)(theta - 20)]`
`B : R'_theta = R'_20 [1 + alpha_B (theta - 20)]`
`R'_theta = R_theta`
`R'_20[1 + alpha_(B)(theta - 20)] = R_20[1 + alpha_(A)(theta - 20)]`
`4[1 + alpha_B(theta - 20)] = 3[1 + alpha_A (theta - 20)]`
`(3 alpha_A - 4 alpha_B)(theta - 20)= 1`
`(3 xx6 -4 xx 2)10^-3(theta - 20)=1`
`theta - 20 = 100`
`theta = 120^@C`.