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Resistors in parallel Two resistors in an electrical
Chapter 12, Problem 59E(choose chapter or problem)
Resistors in parallel Two resistors in an electrical circuit with resistance \(R_{1}\) and \(R_{2}\) 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 \(R_{1}\) with \(R_{2}\) constant affects R.
(d) Describe how a decrease in \(R_{2}\) with \(R_{1}\) constant affects R.
Questions & Answers
QUESTION:
Resistors in parallel Two resistors in an electrical circuit with resistance \(R_{1}\) and \(R_{2}\) 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 \(R_{1}\) with \(R_{2}\) constant affects R.
(d) Describe how a decrease in \(R_{2}\) with \(R_{1}\) constant affects R.
ANSWER:Solution 59E
Step 1 of 8
Consider the effective resistance R of two resistors and
