Resistors in Parallel A resistor in parallel is an element in a circuit where multiple resistors are connected end-to-end, with only a single connection...
A resistor in parallel is an element in a circuit where multiple resistors are connected end-to-end, with only a single connection point. This means that the total resistance of the entire circuit is equal to the sum of the individual resistances of the resistors in parallel.
Here's how it works:
Equivalent resistance: When multiple resistors are connected in parallel, the reciprocal of the total resistance is equal to the sum of the reciprocals of the individual resistances. This means that the total resistance is equal to the reciprocal of the individual resistances.
Equal current: Since the resistors are connected in parallel, the current flowing through the entire circuit is the same for all resistors. This is because the current sources (batteries or power sources) divide the total current equally among the resistors.
Independent variation: Each individual resistor in a parallel circuit has its own resistance, but the total resistance is independent of the individual resistances. This means that the total resistance only depends on the total resistance of the circuit and the resistance of each individual resistor.
Example:
Imagine three resistors with the following values:
R1 = 10 ohms
R2 = 5 ohms
R3 = 15 ohms
If these resistors are connected in parallel, the total resistance would be:
Rtotal = 5 ohms
Therefore, the total resistance of the circuit is 5 ohms, which is equal to the sum of the individual resistances:
This means that the current flowing through the entire circuit is the same, regardless of which resistor is turned on or off