Question

When two resistors are connected in parallel, the effective resistance is given by the expression
1/(1/R_1+1/R_2)
Simplify the complex fraction

Answer 1

The first step is to convert the denominator into a single fraction as follows:
\[\large \frac{1}{R _{1}}+\frac{1}{R _{2}}=\frac{R _{1}+R _{2}}{R _{1}R _{2}}\]
So the effective resistance is now given by:
\[\large \frac{1}{\frac{R _{1}+R _{2}}{R _{1}R _{2}}}\ .........(1)\]
The next step is to multiply the numerator and the denominator of (1) by the reciprocal of the denominator.

Answer 2

The reciprocal of the denominator of (1) is:
\[\large \frac{R _{1}R _{2}}{R _{1}+R _{2}}\]

Answer 3

@TheKavMan Are you following the steps?

Answer 4

@kropot72 so 1*(R1R2)/(R1+R2) correct?

Answer 5

Product over sum. Is a simple method when calculating the total resistance of two resistors connected in parallel.

Answer 6

Thanks alot :)

Answer 7

The simplification is:
\[\large R _{effective}=\frac{R _{1}R _{2}}{R _{1}+R _{2}}\]