Question

The equation represents the total resistance, r, when two resistors

whose resistances are r1 and r2 are connected in parallel. Find the total
resistance when r1 is x and r2 is x + 1.

Answer 1

`R = (x(x+1))/(2x+1)` --- total resistance

Explanation:

Given

`(1)/(R) = (1)/(R_1) + (1)/(R_2)`

Required

Find R when

`R_1 = x`

`R_2 = x+1`

So, we have:

`(1)/(R) = (1)/(R_1) + (1)/(R_2)`

Substitute values for both R's

`(1)/(R) = (1)/(x) + (1)/(x+1)`

Take LCM

`(1)/(R) = (x+1+x)/(x(x+1))`

Collect like terms

`(1)/(R) = (x+x+1)/(x(x+1))`

`(1)/(R) = (2x+1)/(x(x+1))`

Inverse both sides

`R = (x(x+1))/(2x+1)`