Finding equivalent resistance depends on how the resistors are connected in the circuit. The two main types of connections are series and parallel.
Resistors in Series
When resistors are connected in series, they are lined up end-to-end, meaning the same current flows through each resistor. To find the equivalent resistance for resistors in series, you simply add up the individual resistances.
Formula:
Rtotal = R1 + R2 + R3 + ...
Example:
According to the provided reference, an example of finding equivalent resistance in a series is:
The equivalent resistance is the algebraic sum of the resistances (Equation 10.3.2): RS=R1+R2+R3+R4+R5=20Ω+20Ω+20Ω+20Ω+10Ω=90Ω.
In this example, five resistors (four 20Ω resistors and one 10Ω resistor) are connected in series, and the equivalent resistance is calculated as follows:
Rtotal = 20Ω + 20Ω + 20Ω + 20Ω + 10Ω = 90Ω
Resistors in Parallel
When resistors are connected in parallel, they are placed side-by-side, meaning the voltage across each resistor is the same. The equivalent resistance for parallel resistors is calculated differently.
Formula:
1/Rtotal = 1/R1 + 1/R2 + 1/R3 + ...
Simplified Formula for Two Resistors:
Rtotal = (R1 * R2) / (R1 + R2)
Example:
If you have two resistors in parallel, one with a resistance of 10 ohms and the other with a resistance of 20 ohms, the calculation is:
1/Rtotal = 1/10 + 1/20
1/Rtotal = 3/20
Rtotal = 20/3 ≈ 6.67Ω
Summary Table
| Resistor Connection | Formula |
|---|---|
| Series | Rtotal = R1 + R2 + R3 + ... |
| Parallel | 1/Rtotal = 1/R1 + 1/R2 + 1/R3 + ... or Rtotal = (R1 * R2) / (R1 + R2) for two resistors |
Practical Insight
- Understanding equivalent resistance helps in simplifying complex circuits for analysis and design.
- In a series circuit, the equivalent resistance is always greater than the individual resistors.
- In a parallel circuit, the equivalent resistance is always less than the smallest individual resistor.
