Question

From ohms law for circuits, it follows that the total resistance Rtot of two components hooked in parallel is given by the equation
Rtot = R1R2/R1 + R2
where R1 and R2 are the individual resistances.
a) Let R1 = 10 ohms, and graph Rtot as a functon of R2.
b) Find and interpret any asymptotes of the graph obtained in part (a).
c) If R2 = 2 square root R1, what value of R1 will yield an Rtot of 17 ohms?

Answer 1

a) Function Rtot = 10 * R2 / (10 + R2) is the same as

y = 10x/(10 + x)

if y = Rtot and x = R2, so just graph that on a graphing calculator or by hand.

b) The asymptote would be where your graph is undefined because it goes to infinity. How does a function end up going to infinity? What values of x (R1) make this function go to infinity?

c)

\[R2 = 2 \sqrt {R1}\]

Solve for R1

\[R_{Tot} = \frac{R_{1}R_{2}}{R_{1} + R_{2}} = \frac{2R_{1} \sqrt{R_{1}} }{R_{1} + 2\sqrt{R_{1}}} = 17 \Omega\]

Yell if you need help

Answer 2

For b) the V.A.: x= -10? and the H.A.: y = 10? is that right?

im stuck on part c and also how to graph this function.

Answer 3

I don't know what you mean by V.A. and H.A.. x=-10 is an asymptote, yea. Are you flipping everything around and solving for x in terms of y after that? If so you don't need to do that, because it doesn't make physical sense here.

And what about this function are you not able to graph?