Two resistors, one having a positive temperature coefficient of resistance ( + ) and the other having a negative temperature coefficient of resistance ( - ), have the same resistance R₀ at an initial temperature. They are connected in parallel across an ideal battery of constant voltage V . If the temperature of the entire setup is uniformly increased, how will the total power dissipated by the circuit and the power

Step-by-step solution

Let the change in temperature be T . The resistance of the two resistors at the new temperature will be R₁ = R₀(1 + T) and R₂ = R₀(1 - T) . Since they are connected in parallel, the equivalent resistance of the circuit is: R_ eq = R₁ R₂ R₁ + R₂ = R₀^2(1 - ^2 T^2) 2R₀ = R₀ 2 (1 - ^2 T^2) As temperature increases, T increases, so (1 - ^2 T^2) decreases. Thus, the equivalent resistance R_ eq decreases. The total power dissipated by the circuit is P_ total = V^2 R_ eq . Since V is constant and R_ eq decreases, the tota