Answer:
0.1468 ohms per second
Explanation:
You want the rate of change of R when ...
- 1/R = 1/r1 +1/r2
- r1 = 70 Ω
- r2 = 120 Ω
- r1' = 0.3 Ω/s
- r2' = 0.2 Ω/s
Derivative
The desired rate of change is the derivative of R with respect to time. Implicitly differentiating the given relation with respect to time, we have ...
-R'/R² = -r1'/r1² -r2'/r2²
R' = R²(r1'/r1² +r2'/r2²)
Using the given relation and values, we have ...
1/R = 1/70 +1/120 = 190/(70·120)
R = (840/19)
R' = (840/19)(0.3/70² +0.2/120²) = 53/361 ≈ 0.1468
The rate of change of R is about 0.1468 ohms per second.
Additional comment
Most graphing calculators can figure this value for you.