Consider two circuits, (A) and (B), each having two resistors. One of them has a positive temperature coefficient of resistance, + , while the other one has a negative temperature of coefficient, - , 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 :
B. I_A remains constant while I_B increases
For circuit (A), the two resistors are connected in series. The equivalent resistance is given by: R_A = R_0(1 - T) + R_0(1 + T) = 2R_0 The current in circuit (A) is I_A = V R_A = V 2R_0 . Since R_A is independent of the temperature change T, the current I_A remains constant. For circuit (B), the two resistors are connected in parallel. The equivalent resistance is given by: R_B = R_0(1 - T) R_0(1 + T) R_0(1 - T) + R_0(1 + T) R_B = R_0^2(1 - ^2 T^2) 2R_0 = R_0 2 (1 - ^2 T^2) As the temperature increases, T increases, which means the term (1 - ^2 T^2) decreases. Therefore, the equivalent resistance R_B decreases. The current in circuit (B) is I_B = V R_B . Since R_B decreases with an increase in temperature, the current I_B increases. Thus, I_A remains constant while I_B increases. Answer: I_A remains constant while I_B increases
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