How to Use It?
To use the calculator, simply enter the resistance values into the input fields. Initially, there are only two input fields to keep things simple. However, when you click the “Add Resistor” button, a new field will appear. You can add up to eight resistors in this manner.
If you have more than ten resistors, simply use the calculator to determine the equivalent resistance of the first ten resistors, then enter that value into the R1 input field and add values for R11, R12,…, R19 into the R2, R3,…, R10 input fields.
How to Calculate the Equivalent Resistance of a Parallel Resistance Circuit
A parallel resistor circuit is a configuration in which two or more resistors are connected together in parallel.
To calculate the equivalent resistance of resistors connected in parallel, we can use the following formula:
Where:
Req is the equivalent resistance
R1, R2, …, Rn are the individual resistances
The equation is derived from the fact that when resistors are connected in parallel, the voltage across each resistor is the same, but the total current entering the circuit divides among the parallel resistors.
Let’s assume that there are n resistors connected in parallel across a voltage source of V volts. Let Itotal be the total current flowing through the circuit, and I1, I2, … In, be the currents through each resistor.
According to Kirchhoff’s Current Law, the total current flowing through the circuit is the sum of the currents flowing through each resistor. Therefore, we can write:
Since the voltage across each resistor in a parallel circuit is the same, we can express the current flowing through each resistor (using Ohm’s Law) as:
Substituting these expressions into the previous equation, we get:
Factoring out V from the right-hand side, we get:
Dividing both sides by V, we get:
Now, we can define the equivalent resistance of the parallel circuit as the ratio of the voltage to the total current:
Substituting this expression into the previous equation, we get:
Finally, by taking the reciprocal of both sides of the equation, we find the equivalent resistance (Req):
This equation allows us to calculate the equivalent resistance of any number of resistors connected in parallel.
Example
Here is an example of how to calculate the equivalent resistance of a parallel resistor circuit:
Let’s say we have three resistors connected in parallel with values of 10 Ω, 20 Ω, and 30 Ω. Using the equation, we can calculate the equivalent resistance as follows:
Simplifying further:
Therefore, the equivalent resistance of the parallel circuit with resistances of 10Ω, 20Ω, and 30Ω is approximately 5.45Ω.
