h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

So I have a circuit with an unknown current a voltage of 10 and two resistors arranged in parallel

And I am making a simple mathematical error involving summing the reciprocal of the resistance

Which if I solve it the way I've got written down I get the answer 5 Amps.

But I think that contains an error so if I solve it the way I think I get an answer of 20Amps which seems ridiculously high.

So just so I've got the method sorted, would someone mind just running through solving I=V/R for the reciprocal of those two resistors so I can see where I am making my error?

Thanks.

Lets see

You have two resistors, Ra and Rb
The current running through Ra is Ia and that through Rb is Ib
As the resistors are in parallel, the voltage is the same in both, V

The total current running I is the sum of the two currents Ia+Ib

Ia = V/Ra

Ib = V/Rb

I = Ia + Ib
so
I = V/Ra + V/Rb

moving V around because it is common to both, you get
I= V ( (1/Ra) + (1/Rb) )
ie sum the reciprocal of the resistances and multiply by the voltage
loads of brackets in the above just to make sure you get which bits are dived by what and so on