The combined resistance of two resistors R_(1 amd R_2 )in a parallel circuit is given by the formula R_(r= 1/(1/R_1 + 1/R_2 )) Simplify the formula. Help what is this talking about and how do I work it?

find R as a function fo r`1 and r2.

1/R= 1/r1 + `1/R2

R= ???

Get a common denominator on the right (r1r2), combine the fractions, then invert the left and right sides.

r= 1/(1/R_1 + 1/R_2 ) =

R_1 R_2/(R_1 + R_2)

This formula is describing the combined resistance of two resistors, R1 and R2, when they are connected in parallel in an electrical circuit. Resistance is a measure of how easily electric current can flow through a material.

To simplify the formula and find R as a function of R1 and R2, you need to follow these steps:

1. Start with the equation: 1/R = 1/R1 + 1/R2.

2. To get rid of the fractions, find a common denominator for the terms on the right side. The common denominator is R1 * R2.

3. Multiply each fraction by the appropriate denominator to eliminate the fractions:

(1/R) * (R1 * R2/R1 * R2) = (1/R1) * (R1 * R2/R1 * R2) + (1/R2) * (R1 * R2/R1 * R2)


R1 * R2 / (R1 * R2 * R) = (R2) / (R1 * R2) + (R1) / (R1 * R2)

4. Combine the fractions on the right side and simplify:

R1 * R2 / (R1 * R2 * R) = (R2 + R1) / (R1 * R2)

5. Multiply both sides of the equation by the common denominator (R1 * R2 * R) to eliminate the denominator on the left side:

R1 * R2 = (R2 + R1) * R

6. Now, divide both sides of the equation by (R2 + R1) to solve for R:

R = R1 * R2 / (R1 + R2)

Therefore, the simplified formula for the combined resistance R of two resistors R1 and R2 in a parallel circuit is:

R = R1 * R2 / (R1 + R2)