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 Series Resistance Circuit
A series resistor circuit is a configuration in which two or more resistors are connected in series.
To calculate the equivalent resistance of resistors connected in series, 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 series, the current through each resistor is the same, but the voltage drop across each resistor is different.
Let’s assume that there are n resistors connected in series to a voltage source Vtotal. Let V1, V2, … Vn, be the voltage drop across each resistor.
According to Kirchhoff’s voltage law, the algebraic sum of the potential differences in any loop must be zero, so we get:
Using Ohm’s law, we can replace each potential drop with the product of current and resistance:
Factoring out the current, we get:
Rearranging, we get:
Dividing both sides by I, we get:
But we know that the ratio of supply voltage to current is equal to the equivalent resistance of the circuit. That is,
Therefore, we can conclude that:
Example
Here is an example of how to calculate the equivalent resistance of a series resistor circuit:
Let’s say we have three resistors connected in series 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 series circuit with resistances of 10Ω, 20Ω, and 30Ω is 60Ω.
