R = ab/(a+b)

[KevinE]

[FONT=Verdana, Tahoma, Arial, Calibri, Geneva, sans-serif]Ok so my question says:[/FONT]

[FONT=Verdana, Tahoma, Arial, Calibri, Geneva, sans-serif]The use of rearranging formula can help to write them in a form that can be solved.
[/FONT]
[FONT=Verdana, Tahoma, Arial, Calibri, Geneva, sans-serif]The total resistance of two resistors a and b in parallel is given by the formula:[/FONT]


ab
__ = R

a+ b

or R = ab/(a+b)


[FONT=Verdana, Tahoma, Arial, Calibri, Geneva, sans-serif]Given the total resistance is 1.2 ohms and one resistor is 2 ohms. Calculate, using algebra the other resistance.[/FONT]


[FONT=Verdana, Tahoma, Arial, Calibri, Geneva, sans-serif]So I tried multiplying both sides by (a+b)


[/FONT]R(a+b) = a b

then dividing both sides by a

R(a+b)
______ = b
a

I mean obviously the answer is 3. But how to get B on one side...?


I don't know. Help!

 

[Deleted member 4993]

Ok so my question says:

The use of rearranging formula can help to write them in a form that can be solved.

The total resistance of two resistors a and b in parallel is given by the formula:


ab
__ = R

a+ b

or R = ab/(a+b)


Given the total resistance is 1.2 ohms and one resistor is 2 ohms. Calculate, using algebra the other resistance.


So I tried multiplying both sides by (a+b)


R(a+b) = a b

then dividing both sides by a

R(a+b)
______ = b
a

I mean obviously the answer is 3. But how to get B on one side...?


I don't know. Help!

1/R = 1/a + 1/b

1/1.2 = 1/2 + 1/b

1/b = 1/1.2 - 1/2 = ??

and continue....

 

[KevinE]

1/a + 1/b = 0.8333333333333333??? That's not right? I think...

The answer is [FONT=Verdana, Tahoma, Arial, Calibri, Geneva, sans-serif]b = Ra/(a-R)[/FONT]

[FONT=Verdana, Tahoma, Arial, Calibri, Geneva, sans-serif]How to get there will probably cost me the next several days... staring at a computer screen[/FONT]

 

[Ishuda]

\(\displaystyle R = \frac{a b}{a+b}\) ==> \(\displaystyle \frac{1}{R} = \frac{a+b}{a b} = \frac{1}{a} + \frac{1}{b}\)
Thus
\(\displaystyle \frac{1}{b} = \frac{1}{R} - \frac{1}{a} = \frac{a-R}{aR}\)
or
\(\displaystyle b = \frac{aR}{a-R} = \frac{2 * 1.2}{2 - 1.2} = \frac{2.4}{0.8} = 3\)