In this article we will look at series arrangement of resistors. We will also find out when to use this arrangement and how different electrical properties like resistance, voltage, current are affected.
Why combine resistors at all?
Combining resistors in certain ways produce a different equivalent resistance. For example: by using two 10K resistors and arranging them in series, you can obtain an effective resistance of 20K.
You might be wondering: When we can directly buy a resistor of any resistance value, why combine multiple resistors?
Well, generally the resistance of any resistor can vary from a few ohms to mega ohms. And it is not practically feasible to manufacture resistor for each possible resistance. So resistors with only a few standard resistance values are manufactured. And if we require a resistor with resistance anything other than the standard values, we need to combine multiple resistors with standard values in a certain way to get the desired resistance.
Two such types of resistor combinations are series combination of resistors and parallel combination of resistors. There can also be mixed combination of resistors with some groups of resistors connected in series and some others in parallel. In this article we will focus on series arrangement of resistors.
Series Combination of Resistors
Resistors are said to be in series with each other if the end of one resistor is connected to the start of next resistor and so on. Similar to the representation below:
In the above combination of resistors, the end terminal of resistor R1 is connected to the start terminal of resistor R2. Similarly the end terminal of resistor R2 is connected to the start terminal of resistor R3. Any number of resistors can be connected in this way and the whole arrangement can be said as resistors in series with each other.
Also the connection between any two adjacent resistors should be isolated i.e. it should not be connected to any other location in the circuit. Otherwise the resistors can’t be said to be in series.
Electrical Characteristics Resistors in Series
Current always flows through a single path when resistors are connected in series. In the example arrangement illustrated above, current starts from the power source, passes through resistor R1, then through R2 and finally through R3, after which it reaches the power source.
So the values of I1, I2 and I3 are same as the overall current I flowing through the circuit (I = I1 = I2 = I3).
Because a resistor obstructs the flow of current, the potential or voltage of current flowing through any resistor reduces as current flows through it. So the potential / voltage across each resistor depends on it’s resistance.
The overall voltage V will be equivalent to the sum of voltages across each resistor connected in series (V = V1 + V2 + V3).
Formula for Equivalent Resistance of Resistors Connected in Series
Let us derive the equation for the total effective resistance of all the resistors connected in series:
From the observation made in the previous section, we have:
V = V1 + V2 + V3
From Ohm’s law, voltage is equal to the product of current flowing through a resistor and the value of resistance (V = I * R). After assuming that the overall resistance is R and substituting voltages with the equation from ohm’s law, we have the following equation:
IR = I1 * R1 + I2 * R2 + I3 * R3
But from observations in the previous section, we know that current through any resistor connected in series is same as the overall current flowing through the circuit. So I1, I2, I3 can be substituted with I and can be cancelled on LHS and RHS sides. Finally we are left with the below equation:
R = R1 + R2 + R3
The same equation can be extended to any number of resistors connected in series. We just need to add up resistance values of each of the resistors to get the effective resistance of the entire combination.
For example, if resistors 1K, 10K, 47K, 100K are in series, the effective or total resistance will be (1 + 10 + 47 + 100)K, which is equal to 158K. (Note: Instead of writing: 1 Kilo Ohms, we used the short form: 1K)
TODO: Add a basic series resistor calculator for tinkering and some practical examples.
If you have any queries/suggestions, feel free to post them in the comments section of this video: Resistors In Series