- Resistances in Series Definition: A series connection is defined as connecting resistors end to end, so the current flows through each one in turn.
- Series Connection Formula: The total resistance in a series circuit is the sum of all individual resistances.
- Resistances in Parallel Definition: A parallel connection is defined as connecting resistors where each resistor is connected to the same two points, providing multiple paths for the current.
- Parallel Connection Formula: The equivalent resistance in a parallel circuit is found using the formula 1/R = 1/R1 + 1/R2 + 1/R3.
- Resistance Connection Impact: How resistors are connected (series or parallel) affects the total resistance and current flow in a circuit.
More than one electrical resistance can be connected in series, in parallel, or in a combination of both. Here, we will mainly discuss series and parallel connections.
Resistances in Series
Suppose you have three different types of resistors – R1, R2 and R3 – and you connect them end to end as shown in the figure below, then it would be referred as resistances in series. In case of series connection, the equivalent resistance of the combination, is sum of these three electrical resistances.
This means the resistance between points A and D is the sum of the three individual resistances. The current enters at point A and leaves at point D because there are no parallel paths in the circuit.
Let’s say the current is I. This current will pass through resistors R1, R2 and R3. Using Ohm’s law, the voltage drops across the resistors are V1 = IR1, V2 = IR2 and V3 = IR3. If the total voltage across the series combination is V, then:
Then obviously
Since, sum of voltage drops across the individual resistance is nothing but the equal to applied voltage across the combination.
Now, if we consider the total combination of resistances as a single resistor of electric resistance value R, then according to Ohm’s law,
V = IR ………….(2)
Now, comparing equation (1) and (2), we get
So, the above proof shows that equivalent resistance of a combination of resistances in series is equal to the sum of individual resistance. If there were n number of resistances instead of three resistances, the equivalent resistance will be 
Resistances in Parallel
Suppose we have three resistors with resistance values R1, R2 and R3. These resistors are connected so that each terminal is connected together, forming a parallel circuit.
This combination is called resistances in parallel. If electric potential difference is applied across this combination, then it will draw a current I (say).
As this current will get three parallel paths through these three electrical resistances, the current will be divided into three parts. Say currents I1, I1 and I1 pass through resistor R1, R2 and R3 respectively.
Where total source current
Now, as from the figure it is clear that, each of the resistances in parallel, is connected across the same voltage source, the voltage drops across each resistor is the same, and it is same as supply voltage V (say).
Hence, according to Ohm’s law,
Now, if we consider the equivalent resistance of the combination is R.
Then, 
Now putting the values of I, I1, I2 and I3 in equation (1) we get,
The above expression represents equivalent resistance of resistor in parallel. If there were n number of resistances connected in parallel, instead of three resistances, the expression of equivalent resistance would be
