Equivalent resistance in series
Resistors in a row add up.
One resistor in place of three
Three resistors of 2 Ω, 3 Ω and 5 Ω are joined in series. We want one single resistor that can take their place without changing the current.
What should the resistance of that single resistor be?
What this lesson covers
The idea
Resistors in series can be replaced by an equivalent resistance Rs = R1 + R2 + R3, the sum of the individual resistances, which is greater than any individual resistance.
One resistor in place of three
Three resistors of 2 Ω, 3 Ω and 5 Ω are joined in series. We want one single resistor that can take their place without changing the current.
What should the resistance of that single resistor be?
- 10 Ω, the sum of the three
- 5 Ω, the biggest of the three
- Less than 2 Ω
Add the blocks
Change each resistance with the plus and minus buttons. The long block is the single resistor that can replace the three.
A sum, and always bigger
The long block was always as long as the three blocks together. So it is bigger than any one block.
Resistors in series can be replaced by an equivalent resistance Rs = R₁ + R₂ + R₃, the sum of the individual resistances. It is greater than any individual resistance.
Notes
Resistors in series have an equivalent resistance Rs = R₁ + R₂ + R₃, the sum, which is greater than any individual resistance.
Check yourself
An electric lamp of 20 Ω and a conductor of 4 Ω are joined in series. What is the total resistance, in Ω?
Answer: 24 Ω
Rs = R₁ + R₂ = 20 Ω + 4 Ω = 24 Ω.
Three resistors of 2 Ω, 3 Ω and 5 Ω are joined in series. What is their equivalent resistance, in Ω?
Answer: 10 Ω
Rs = 2 Ω + 3 Ω + 5 Ω = 10 Ω.
How does the equivalent resistance of resistors in series compare with each individual resistance?
A third resistor is joined in series with two resistors. What happens to the total resistance?
- It is smaller than all of them. In series the resistances add, so the total is greater than each one.
- It is greater than any of them — correct. Yes!
- It is equal to the smallest of them. The total is the sum of all, so it is greater than the smallest, and greater than any individual resistance.
- It decreases. Adding a resistor in series adds its resistance to the sum, so the total increases.
- It stays the same. The total is R₁ + R₂ + R₃, so a new term changes it.
- It increases — correct. Yes!