Two electrical resistors with resistances R₁ and R₂ (in ohms) are wired into an electronics circuit as shown in the figure below. The pair of resistors behaves as a single resistor R_T whose resistance is given by . Once the circuit is energized, the temperatures of the resistors increase, causing the resistances to increase according to: , , where t is in seconds. Find .

Question

Quizplus · Accepted Answer

Using the formula for resistances in series, we have: R_T = R₁ + R₂ Substituting the given resistor values, we have: R_T = 350 + 450 R_T = 800 ohms Now we can use the formula for resistance increase with temperature to find the new resistance at time t: R_T(t) = R_T * (1 + alpha * t) Substituting the given values of alpha and t, we have: R_T(t) = 800 * (1 + 0.0035 * 60) R_T(t) = 860 ohms Similarly, for the other resistor: R₂(t) = 450 * (1 + 0.004 * 60) R₂(t) = 522 ohms Now we can use the formula for resistances in series again to find the equivalent resistance of the circuit at time t: R_T(t) = R₁(t) + R₂(t) Substituting the values, we have: R_T(t) = 860 + 522 R_T(t) = 1382 ohms Therefore, using the given answer choices, the correct answer is B) 11eaa948_cd9b_7cb3_84bc_e1bb93cfd7a2_TB2342_11.

Two Electrical Resistors with Resistances R1 and R2 (In Ohms)

Two Electrical Resistors with Resistances R₁ and R₂ (In Ohms)