combination of resistance| resistance in series | resistance in parallel |

Apart from potential difference, current in a circuit depends on resistance of the circuit.
So, in the electrical circuits of radio, television and other similar things, it is usually necessary to combine two or more resistances to get the required current in the circuit.
We can combine the resistances lengthwise (called series) or we can put the resistances parallel to one another.

Thus, the resistances can be combined in two ways :
in series, and
(ii) in parallel.
If we want to increase the total resistance, then the individual resistances are connected in series, and if we want to decrease the resistance, then the individual resistances are connected in parallel.
When two (or more) resistances are connected end to end consecutively, they are said to be connected in series.
on the other hand, when two (or more) resistances are connected between the same two points, they are said to be connected in parallel (because they become parallel to one another).
The combined resistance (or resultant resistance) of a number of resistances or resistors connected in series is calculated by using the law of combination of resistances in series.
According to the law of combination of resistances in series : The combined resistance of any number of resistances connected in series is equal to the sum of the individual resistances.
For example, if a number of resistances R1, R2, R3 ...... etc., are connected in series, then their combined resistance R is given by : R = R1 + R2 + R3 +.........
Suppose that a resistance R1 of 2 ohms and another resistance R2 of 4 ohms are connected in series and
we want to find out their combined resistance R.
We know that : So, And, R = R1 + R2 R = 2 + 4 Combined resistance, R = 6 ohms
Thus, if we join two resistances of 2 ohms and 4 ohms in series, then their combined resistance (or resultant resistance) will be 6 ohms which is equal to the sum of the individual resistances.
Before we derive the formula for the resultant resistance of a number of resistances connected in series, we should keep in mind that :
(i) When a number of resistances connected in series are joined to the terminals of a battery, then each resistance has a different potential difference across its ends (which depends on the value of resistance).
But the total potential difference across the ends of all the resistances in series is equal to the voltage of the battery.
Thus, when a number of resistances are connected in series, then the sum of the potential differences across all the resistances is equal to the voltage of the battery applied.
(ii) When a number of resistances are connected in series, then the same current flows through each resistance (which is equal to the current flowing in the whole circuit).
two resistances R1 and R2 connected in series. A battery of V volts has been applied to the ends of this series combination.
Now, suppose the potential difference across the resistance R1 is V1 and the potential difference across the resistance R2 is V2.
We have applied a battery of voltage V, so the total potential difference across the two resistances should be equal to the voltage of the battery.
That is : V = V1 + V2 ... (1)
We have just seen that the total potential difference due to battery is V.
Now, suppose the total resistance of the combination be R, and the current flowing through the whole circuit be I.
So, applying Ohm’s law to the whole circuit, we get
Since the same current I flows through both the resistances R1 and R2 connected in series, so by applying Ohm’s law to both the resistances separately, we will get :
Now, putting the values of V, V1 and V2 from equations (2), (3) and (4) in equation (1), we get :
Cancelling I from both sides, we get :
Resultant resistance (combined resistance or equivalent resistance),
R =R1 + R2
The combined resistance (or resultant resistance) of a number of resistances or resistors connected in parallel can be calculated by using the law of combination of resistances in parallel.
According to the law of combination of resistances in parallel : The reciprocal of the combined resistance of a number of resistances connected in parallel is equal to the sum of the reciprocals of all the individual resistances.
For example, if a number of resistances, R1, R2, R3 ...... etc., are connected in parallel, then their combined resistance R is given by the formula




Suppose that a resistance R1 of 6 ohms and another resistance R2 of 12 ohms are connected in parallel and we want to find out their combined resistance R.
So, Combined resistance, R = 4 ohms
This means that if we join two resistances of 6 ohms and 12 ohms in parallel then their combined resistance is only 4 ohms which is less than either of the two individual resistances (of 6 ohms and 12 ohms).
Thus, when a number of resistances are connected in parallel then their combined resistance is less than the smallest individual resistance.