# Calculating R with 2 resistors parallel

I've ran into a slight confusion.

The equation for resistance in a parallel circuit should work for any number of resistors, I assumed. So when I'd have 2 resistors in parallel, total Rt would be: Rt = 1/G and G=1/Ra + 1/Rb

Now my book says, for 2 resistors in parallel, you may use this formula too: Rt = (Ra * Rb) / (Ra + Rb)

When I fill in 100 Ohms for Ra, and 220 Ohms for Rb, the two equations produce different results. (68.75 for the first, and 66.67 for the second). Now, I have tried it with several sets of values, but I couldn't reproduce this difference with those.

What is happening!? I'm lost!

Edit: Yeah, I've been miscalculating indeed. How embarrassing to find out this way. Thanks for all your answers :)

• Please check your maths. Those equations are mathematically equivalent. I get 66.67 if I wrongly enter the Ra+Rb as 230 Ohms instead of 220. – akellyirl Sep 22 '14 at 11:03
• I got the same as @akellyirl - and then read his answer. ie 100 x 220 / (100+**230**) = 66.67 . ie you have simply misentered one figure. – Russell McMahon Sep 22 '14 at 11:05
• If you get a "wrong" answer ALWAYS recalculate and watch your input. Best is to try to find some other way to enter the data. eg here you could try 22000/320 as doing that much "in your head" is easy – Russell McMahon Sep 22 '14 at 11:08
• I sometimes make mistakes with a dumb-calculator, so I use a spreadsheet or a calculator which records every step (on my Mac). The spreadsheet is a very good approach as I can ensure the same values are always used. It saves a lot of gnnnnnggg. – gbulmer Sep 22 '14 at 11:17

$$\frac{100 \cdot 220}{100 + 220} = \frac{1}{\frac{1}{100} + \frac{1}{220}} = 68.75$$
$$\frac{1}{\frac{1}{R_1} + \frac{1}{R_2}} = \frac{1}{\frac{1}{R_1} + \frac{1}{R_2}}\frac{R_1\cdot R_2}{R_1\cdot R_2}=\frac{R_1\cdot R_2}{R_1 + R_2}$$