Part of a circuit has two resistors connected in parallel as shown in the figure. R(1) is a constant resistor of 10 ohm, while R(2) is a variable resistor with resistance that varies at a rate of 2 ohms per minute. The total, or effective, resistance, R, provided by this circuit is given by:

Question

1/R=1/R(1)+1/R(2)

At what rate does the effective resistance change when R(2) is 100 ohms? Round off your answer to four decimal places

Answer 1

R = R1 R2/(R1+R2)
R1 is constant
dR = R1 [(R1+R2) dR2- R2 dR2]/ (R1+R2)^2

dR/dt = R1 dR2/dt [R1]/(R1+R2)^2

dR/dt = 100(2) /(110)^2

Answer 2

0.0165