HOW TO CALCULATE EQUIVALENT RESISTANCE
This set of instructions will teach you how to calculate a circuit’s equivalent resistance.
Equivalent resistance is the total resistance of a circuit, calculated as if all resistors were
combined into one.
RESISTORS IN SERIES
The most basic formation of resistors is called series formation. This formation allows current to
flow from one resistor to the next. In series, resistors all have the same current flow through
them. Below are two resistors in a series formation.
CALCULATING E QUIVALENT RESISTANCE OF RESISTORS IN SERIES
-
Resistors in series can be added together to find their equivalent resistance.
o Req = R1 + R2 + … + Rn (where Rn is the nth resisitor in the formation)
Through this method of calculation, you can combine the two 100-Ohm resistors
can to form one 200-Ohm resistor as shown below.
RESISTORS IN PARALLEL
Another formation of components is parallel formation. Resistors in this formation branch apart
at one point and are joined again at another point in the circuit. In a parallel formation, current
flows through each resistor in different amounts. Below are two resistors in a parallel
formation.
NOTE: There are combinations that allow resistors in parallel to have the same current flow.
This is dependent on the value of resistance in each resistor and will not be covered in these
instructions.
CALCULATING E QUIVALENT RESISTANCE OF RESISTORS IN PARALLEL
-
Resistors in parallel require a bit more calculation to find their equivalent
resistance. The formula below shows how to do this.
1
th
o Req = 1 1
1 (Where Rn is the n resistor in the formation)
-
Another formula that is much simpler to use is shown below.
𝑅1∗𝑅2
o Req = 𝑅1+𝑅2
+
𝑅1 𝑅2
+…+
𝑅𝑛
CAUTION: This formula is applicable when calculating equivalent resistance of two resistors in
parallel. Calculations will be incorrect if more than two resistors are used.
-
Through this method, you can combine the two 100-Ohm resistors to form one
50-Ohm resistor as shown below.
COMBINATIONAL CIRCUITS
Combinational circuits are circuits that use both series and parallel formations. These are much
more common than individual series or parallel circuits. Equivalent resistance can be calculated
by using both series and parallel calculations to portions of the circuit that that they apply to.
FINDING EQUIVALENT RESISTANCE OF A COMBINATIONAL CIRCUIT
The combinational circuit shown below can be simplified to one equivalent resistance.
Please follow the steps provided to see how this is done.
1. Combine R1 and R2 that are in series:
o R1-2 = R1 + R2 = 100 + 100 = 200 Ohms
o Then simplify the circuit to:
2. Combine R1-2 and R4 that are in paralle:
(𝑅1−2)∗𝑅4
(𝑅1−2)+𝑅4
200∗100
200+100
o
R1-2-4 = =
o
Then simplify the circuit to:
==
= 66.7 Ohms
3. Combine R1-2-4 and R3 that are in series:
o Req = R1-2-4 + R3 = 66.7 + 100 = 166.7 Ohms
o Then simplify the circuit to: