Chapter 12.4, Problem 75E

Resistors in parallel Two resistors in an electrical circuit with resistance R₁ and R₂ wired in parallel with a constant voltage give an effective resistance of R, where $\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}$.

a.    Find $\frac{\partial R}{\partial R_1}$ and $\frac{\partial R}{\partial R_2}$ by solving for R and differentiating.

b.    Find $\frac{\partial R}{\partial R_1}$ and $\frac{\partial R}{\partial R_2}$ by differentiating implicitly.

 c.    Describe how an increase in R₁ with R₂ constant affects R.

 d.    Describe how a decrease in R₂ with R₁ constant affects R.