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 :)

  • \$\begingroup\$ 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. \$\endgroup\$
    – akellyirl
    Sep 22, 2014 at 11:03
  • \$\begingroup\$ 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. \$\endgroup\$
    – Russell McMahon
    Sep 22, 2014 at 11:05
  • \$\begingroup\$ 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 \$\endgroup\$
    – Russell McMahon
    Sep 22, 2014 at 11:08
  • \$\begingroup\$ 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. \$\endgroup\$
    – gbulmer
    Sep 22, 2014 at 11:17

1 Answer 1


What is happening!?

You made a calculation error.

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

It's easy to show the equivalence of the two formula:

$$\frac{1}{\frac{1}{R_1} + \frac{1}{R_2}} = \frac{1}{\frac{1}{R_1} + \frac{1}{R_2}}\frac{R_1\cdot R_2}{R_1\cdot R_2}=\frac{R_1\cdot R_2}{R_1 + R_2}$$

  • \$\begingroup\$ Yep... It just took me a while to find out.. adding 100 and 220 to 330 felt so natural at the time \$\endgroup\$
    – Smokez
    Sep 22, 2014 at 11:06

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.