A resistance R with temperature coefficient α is connected in parallel with a resistance 3R having temperature coefficient 2α. If the effective temperature coefficient is α(eff) = (k/4)α, find k.
Physics · Current electricity · Electric Current, Drift Velocity & Resistance
JEE Mains

Question

A resistance R with temperature coefficient α is connected in parallel with a resistance 3R having temperature coefficient 2α. If the effective temperature coefficient is α(eff) = (k/4)α, find k.

G1 Physics · Accepted Answer

For two parallel resistors, differentiate the total conductance with temperature. With R and 3R having coefficients α and 2α, the effective coefficient is α(eff)=5α/4. Therefore k=5.