Two electrical resistors (one of variable resistance x and one with fixed resistance R1) are put in parallel into a circuit. The combined resistance R, of those two resistors is given by the formula (1/R) = (1/x) + (1/R1). Solve this equation for R. Your answer will be a rational function in x and will include the constant R1. Determine the horizontal asymptote of this function when R1=2000 ohms and then answer the question: As the resistance of x approaches infinity, what is the combined resistance of the two resistors parallel?
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First part. Since we are dealing with only two resistors, R1 and Rx we can use the product over sum to obtain the equivalent resistance R.
R=(R1)(Rx)/(R1 + Rx).
For the second part where R1=2000 Ohms and Rx is allowed to increase without limit, R will approach a value of 2,000 Ohms
Please note when only two resistors are connected in parallel
Rtotal= 1(1/R1 + 1/R2) which will work down to being product over sum
Rtotal = R1R2/(R1+R2)