Series Connection of Resistors

Concept Explanation

Series Connection of Resistors

Combination of Resistance:

In many applications to get a required value of resistance two or more resistances are combined. Two or more resistance can be combined in more than one way.

1. Series Combination

2. Parallel Combination

If, in an electrical circuit, two or more resistances connected between two points are replaced by a single resistance such that there is no change in the current of the circuit and in the potential difference between those two points, then the single resistance is called the 'equivalent resistance. When the resistance of a circuit is to be increased, they are combined in series and when heavy current is to be passed they are combined in parallel so as to decrease the total resistance.

Series Combination of Resistance:

In this combination, the resistances are joined end to end. Thus the second end of each resistance is joined to the first end of the next resistance, and so on. The first end of the first resistance and the second end of the last resistance are connected to the cell. In this combination, the same current flows in all the resistances but the potential differences between their ends are different according to their resistances.

In this combination more than one resistance is connected one after the other as shown. In this type of circuit:

1. Equal current flows through each resistance.

2. Total voltage drop across the combination is equal to the sum of voltage drop across each resistance.

3. Voltage drop each resistance can be calculated using Ohm’s Law and is proportional to the value of resistance.

4. Equivalent resistance is thus greater than resistance of any resistor in the circuit.. This is also known as maximum effective resistance

In the circuit given we have three resistance R₁, R₂ and R₃ are connected in series and V₁, V₂ and V₃ are the potential drop across each resistance respectively. If I is the current flowing through the circuit when a cell with potential difference V is applied across them

$V_1= I R_1$ .......(1)

$V_2= I R_2$ .......(2)

$V_3= I R_3$ .......(3)

Now, let us assume a resistance $R_s$ is the equivalent resistance which will have the same potential difference as the combination.

$V= I R$ .......(4)

Equivalent resistance can be calculated by using the fact that total potential drop in the circuit is equal to the sum of potential drop across each resistance

$V= V_1+V_2+V_3$ .......(5)

Substituting the value from Equations 1, 2, 3, 4 in 5 we get

$I R_s =I R_1 + I R_2 + I R_3$

$I R_s =I (R_1 + R_2 + R_3)$

$R_s = R_1 + R_2 + R_3$

The sum of individual potential drop across the resistors connected in series is equal to the total potential difference across the series can be derived as follows

Potential difference across point A and B $R_1 ;i.e.; V_1 = V_A - V_B$

Potential difference across point B and C $R_2 ;i.e.; V_2 = V_B - V_C$ ,

Potential difference across Point C and D $R_3 ;i.e.; V_3 = V_C - V_D$

On adding the potentials across $R_1, ;R_2 ;and ;R_3$

$V_1 + V_2 + V_3 = (V_A - V_B) + (V_B -V_C) + (V_C- V_D)=V_A-V_D$

i.e. equal to the potential difference between points A and D = V

Disadvantages of Series Combination:

(i) In series combination, if any of the components fail to work, the circuit will break and then none of the components will work.

(ii) It is not possible to connect a bulb and a heater in series because they need different values of current to operate properly. Hence, to overcome this problem we do not use series circuit.

Illustration: Five resistance are connected as shown in the figure below. Calculate current through the circuit, also calculate the potential drop across resistance R₅

Solution: In the figure we are given five resistances which are connected in series. To calculate current in the circuit we have to calculate the equivalent resistance.

The equivalent resistance is the sum of individual resistance

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Sample Questions

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Question : 1

A bulb, fan, and a motor each of resistance of 13 ohm,25 ohms and 40 ohms are connected in series.The effective resistance will be
A. 78 ohm	B. Between 75 ohm and 80 ohm	C. Between 72 ohm and 79 ohm	D. All of these
Right Option : D
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Question : 2

Three resistance of 3 ohm, 1 ohm and 2 ohm are connected in series.How much potential difference should be applied is a current 3mA is allowed to flow.
A. 1.8mV	B. 0.018 V	C. 0.0018 V	D. None of these
Right Option : B
View Explanation

Question : 3

A bulb, fan, and a motor each of resistance of 13 ohm,25 ohms and 40 ohms are connected in series.How much potential difference should be applied to make 15A of current to flow through the circuit.
A. $large 1.17 X 10^{6} mV$	B. 1.17 KV	C. 1170 V	D. All of these
Right Option : D
View Explanation