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Consider two circuits, (A) and (B), each having two resistors. One of them has a positive temperature coefficient of resistance, $+\alpha$, while the other one has a negative temperature coefficient, $-\alpha$, as shown in the figure. The current through these circuits are denoted by $I_A$ and $I_B$. At initial temperature, the resistance of the two resistors is $R_0$. As the temperature is increased, the correct option that describes the variation of current in these circuits is:
Detailed Solution
Circuit A (series): $R_A=R_0(1+\alpha\Delta T)+R_0(1-\alpha\Delta T)=2R_0$, so $I_A=\frac{V}{2R_0}$ does not depend on temperature. Circuit B (parallel): $R_B=\frac{R_0^2(1+\alpha\Delta T)(1-\alpha\Delta T)}{2R_0}=\frac{R_0}{2}(1-\alpha^2\Delta T^2)$. As $\Delta T$ increases, $R_B$ decreases, so $I_B$ increases.