Physics

Physics

Problem

A circuit contains two resistors in series connected to an ideal battery: • Rmetal=100 ΩR_{\text{metal}} = 100\,\Omega at 25 ∘C25\,^{\circ}\text{C}, made of a typical metal whose resistance increases with temperature. • Rtherm=100 ΩR_{\text{therm}} = 100\,\Omega at 25 ∘C25\,^{\circ}\text{C}, made of a material whose resistance decreases with temperature. When the circuit operates, both resistors reach 35 ∘C35\,^{\circ}\text{C}. At this temperature, RmetalR_{\text{metal}} has increased by 5%5\%, and RthermR_{\text{therm}} has decreased by 10%10\%. Which statement best describes what happens to the magnitude of the current after the temperature rise? a) The current decreases because the metal resistor’s 5%5\% increase in resistance makes the total resistance larger. b) The current is essentially unchanged because the two equal-but-opposite percentage changes offset one another. c) The current increases slightly because the total series resistance becomes smaller (about 2.5%2.5\% lower). d) The current increases by about 10%10\% because the thermistor’s larger percentage decrease in resistance dominates the circuit.

Browse the problem library