The total resistance in a parallel circuit is calculated by taking the reciprocal of the sum of the reciprocals of each individual resistance.
Understanding Parallel Circuits
In a parallel circuit, the current has multiple paths to flow through. This means that the voltage across each resistor is the same, but the current through each resistor can be different.
Calculating Total Resistance
Here's the formula to calculate the total resistance (R<sub>T</sub>) in a parallel circuit:
1/R<sub>T</sub> = 1/R<sub>1</sub> + 1/R<sub>2</sub> + 1/R<sub>3</sub> + ...
Where:
- R<sub>T</sub> is the total resistance of the circuit
- R<sub>1</sub>, R<sub>2</sub>, R<sub>3</sub>... are the resistances of each individual resistor in the circuit
Example
Let's say you have three resistors in parallel:
- R<sub>1</sub> = 10 ohms
- R<sub>2</sub> = 20 ohms
- R<sub>3</sub> = 30 ohms
To find the total resistance:
- Calculate the reciprocal of each resistance:
- 1/10 = 0.1
- 1/20 = 0.05
- 1/30 = 0.0333
- Add the reciprocals together:
- 0.1 + 0.05 + 0.0333 = 0.1833
- Take the reciprocal of the sum:
- 1/0.1833 = 5.45 ohms
Therefore, the total resistance of the circuit is 5.45 ohms.
Key Points
- Total resistance in a parallel circuit is always less than the smallest individual resistance.
- As you add more resistors in parallel, the total resistance decreases.
- The formula can be applied to any number of resistors in parallel.
