Parallel circuit equation question

[Daizzy]

I am starting a course in Sept in electrical installation. As it's been a while since I left full time education I thought I would buy the relevant textbook to give me a head start and get my brain into gear.

My problem relates to parallel circuit calculation!

Example: three resistors of 16, 24, and 48 ohms are connected across a 240v supply find the the total resistance. I know that it's 8 ohms because it tells me so. What I don't understand is how that is arrived at.
the equation is shown like this:
1/Rt= 1/R1+1/R2+1/R3 = 1/16 + 1/24 + 1/48
and therefore:
1/Rt = 3+2+1/48 = 6/48
I realize that 48/6 =8 what I don't get is what does 1 represent and where does 48 come from as in: 3+2+1/48

There is no explanation of how the calculation is done!

Homework Equations

The Attempt at a Solution

 

[salman213]

well the there are basically two ways u can add resistors

one way is in series the general formula for that is

Rt = R1+R2+R3 (considering there are 3 resistors)

if the resistors are set up in parallel then the formula you use changes to

1/Rt = 1/R1 + 1/R2 + 1/R3

and so solve for RT.

you have 1/Rt to find Rt you take the inverse.

 

[Daizzy]

Thanks for that, that's much simpler than what's written in this book!

So: 1/16=0.0625 1/24=0.041 1/48=0.020
therefore: 0.0625+0.041+0.020=8

Have I got it right?

 

[dlgoff]

Note that Rt=R1R2R3/(R1+R2+R3)

 

[Defennder]

Thanks for that, that's much simpler than what's written in this book!

So: 1/16=0.0625 1/24=0.041 1/48=0.020
therefore: 0.0625+0.041+0.020=8

Have I got it right?

Yeah but you omitted the part where you take the reciprocal to get 8 ohms.

 

[dlgoff]

Note that Rt=R1R2R3/(R1+R2+R3)

Sorry about that. This is not correct.

 

[Daizzy]

Yeah but you omitted the part where you take the reciprocal to get 8 ohms.

Yes I forgot to inclucde 1/0.1235 = 8 totally missed it out when I was typing!

Thanks for everyone's help, I think my brain is finally engaging!