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:
[tex]\large {\boxed {R_s = R_1 + R_2 + R_3 + ...} }[/tex]
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:
[tex]\large {\boxed {\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ...} }[/tex]
Let's tackle the problem now !
Given:
Resistance 1 = r₁
Resistance 2 = r₂
Unknown:
Total Resistance = R
Solution:
This problem is about Parallel Circuit.
[tex]\frac{1}{R} = \frac{1}{r_1} + \frac{1}{r_2}[/tex]
[tex]\frac{1}{R} = \frac{r_2}{r_1r_2} + \frac{r_1}{r_1r_2}[/tex]
[tex]\frac{1}{R} = \frac{r_1 + r_2}{r_1r_2}[/tex]
[tex]R(r_1 + r_2) = r_1 r_2[/tex]
[tex]R = (r_1 r_2) \div (r_1 + r_2)[/tex]
[tex]R = \large \boxed {\frac{r_1 r_2}{r_1 + r_2}}}[/tex]
Learn more
- The three resistors : https://brainly.com/question/9503202
- A series circuit : https://brainly.com/question/1518810
- Compare and contrast a series and parallel circuit : https://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
