The combined resistance of two resistor is given by....

[dkarolasz]

The combined resistance of two resistor R1 and R2 in the parallel circuit is given by the formula

1
Rr= ________
1 1
___+_____
R1 R2

Simplify the formula

?????[/i][/b]

 

[soroban]

Re: word problem

Hello, dkarolasz!

The combined resistance of two resistor \(\displaystyle R_1\) and \(\displaystyle R_2\)
in the parallel circuit is given by the formula:

. . \(\displaystyle \L R_r\;=\;\frac{1}{\frac{1}{R_1}\,+\,\frac{1}{R_2}}\)

Simplify the formula

Multiply top and bottom by \(\displaystyle R_1R_2\)

. . \(\displaystyle \L R_r\;=\;\frac{R_1R_2}{R_1R_2}\,\cdot\,\frac{1}{\frac{1}{R_1}\,+\,\frac{1}{R_2}} \;=\;\frac{R_1R_2}{R_1R_2\left(\frac{1}{R_1}\,+\,\frac{1}{R_2}\right)}\)

. . \(\displaystyle \L R_r\;=\;\frac{R_1R_2}{R_2\,+\,R_1}\)