Question

R(r1+r2)=r1r2 solve for R

Answer 1

R(r+r^2)=(r)(r^2)
R^2+r^3=r^3
R^2=0
R=0

Answer 2

R = ( r₁ r₂ ) ÷ ( r₁ + r₂ )

Further explanation

Electrical circuits can generally be divided into two types , i.e :

1. Series Circuit

In series circuit, the electric current flowing on each resistor is always the same as the total current.

To find the total resistances you can use the following formula:

$\large {\boxed {R_s = R_1 + R_2 + R_3 + ...} }$

2. Parallel Circuit

In parallel circuits, the electrical voltage at each resistor is always the same as the source voltage.

To find the total resistances you can use the following formula:

$\large {\boxed {\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ...} }$

Let's tackle the problem now !

Given:

Resistance 1 = r₁

Resistance 2 = r₂

Unknown:

Total Resistance = R

Solution:

This problem is about Parallel Circuit.

$\frac{1}{R} = \frac{1}{r_1} + \frac{1}{r_2}$

$\frac{1}{R} = \frac{r_2}{r_1r_2} + \frac{r_1}{r_1r_2}$

$\frac{1}{R} = \frac{r_1 + r_2}{r_1r_2}$

$R(r_1 + r_2) = r_1 r_2$

$R = (r_1 r_2) \div (r_1 + r_2)$

$R = \large \boxed {\frac{r_1 r_2}{r_1 + r_2}}}$

Learn more

• The three resistors : brainly.com/question/9503202
• A series circuit : brainly.com/question/1518810
• Compare and contrast a series and parallel circuit : brainly.com/question/539204

Answer details

Grade: High School

Subject: Physics

Chapter: Current of Electricity

Keywords: Series , Parallel , Measurement , Absolute , Error , Combination , Resistor , Resistance , Ohm