Series Arrangements of Resistances and Cells

Introduction 

The graphical representation of the electrical circuit is known as a circuit diagram. In a circuit diagram, the essential components are cell/battery, resistance, ammeter, voltmeter, electrical device and a switch. The cell is the generator of electricity through a chemical reaction. Its purpose is to maintain a potential difference so as to ensure the continuous flow of current. At the same time, resistance is the restriction that is offered to the flow of current. This article aims to provide a general knowledge of the series arrangement of resistance and cells. 

Internal resistance of cell 

In an electric circuit, there can be two types of resistance. The normal resistance is the usual resistance that is offered. The next is the resistance within the battery itself, known as internal resistance. 

The internal resistance is an obstruction to the flow of current due to the electrodes of the cell. It is found in the battery or the cell. 

The internal resistance of the cell depends on: 

• Nature of electrolyte
• Concentration of electrolyte
• Distance between the electrodes
• Varies inversely to temperature 

Types of arrangement of resistance and cell

There are two basic and easy ways to connect or arrange the cells and resistance in a circuit diagram. These are: 

• Series Combination 
• Parallel Combination 

In this article, we will be learning about the series arrangement of resistance and cells. But before that, we will recall Ohm’s Law. Which states that: 

“The current flowing through a circuit is directly proportional to the potential difference across the terminal of the cell.” 

Mathematically, we get: 

V ∝ I

V = IR

Here, 

V is the potential difference 

I is the current

R is the resistance 

Series Arrangement of Cells

When the cells in a circuit are connected end to end, the arrangement is a series combination. The same current is flown through each cell. 

Thus if a circuit has ‘n’ number of cells with emf E1, E2 till En, combined together, then the effective (total) emf of the cell E becomes: 

E = E1 + E2 + E3+……..+En

Series Arrangement of Resistance 

In a series arrangement of the resistance, all the resistances are connected end to end. Therefore, the same current flows through all the resistance, but the potential drop differs. 

If we have ‘n’ number of resistance connected in series. The individual resistance are R1, R2, R3, . . . . . , Rn and the potential drops are V1, V2, V3, . . . , V3. 

Using Ohm’s law, we have a total potential of the circuit as have: 

V=IR

The potential drop at the individual resistances will be: 

V1= IR1

V2= IR2

V3= IR3

……..

Vn = IRn

Thus total potential would be:

V = V1+V2+V3+…….+ Vn

IR = IR1+ IR2+IR3+…….+ IRn

R = R1+ R2+R3+…….+ Rn

This is the formula of the total resistance in the series combination. 

Advantages and disadvantages of series combination of cell and resistance

There are various advantages and disadvantages of connecting cells and resistance in a series combination. The advantages are as follow:

• They do not heat that efficiently, thus, any explosive device does not catch fire when kept near the circuit. 
• Current remains the same throughout the combination, thus, all the appliances connected get a sufficient amount of current. 

However, apart from these few advantages, there are various drawbacks of connecting the cells and resistance in a series combination. These are: 

• The most significant disadvantage of series combination is that any break or fault in the appliance completely cuts off the current supply for all the other appliances. 
• A series combination needs more wiring to complete the circuit and the voltage can not be increased. To increase the voltage, one needs to decrease the resistance. 

Solved Examples

1. Find the resultant resistance for the given circuit. 

Solution: 

R1 = 5 ohm

R2 = 3 ohm

R3 = 2 ohm

Resultant resistance of the circuit would be: 

R = R1 + R2 + R3

R = 5 + 3 + 2

R = 10 ohm

1. Find the current flowing through the circuit. 

V = 40 V

R1 = 6 ohm

R2 = 4 ohm

Resultant resistance of the circuit:

R = R1 + R2

R = 6 + 4 ohm

R = 10 ohm 

According to ohm’s law: 

V = IR

I =VR

I = 4010

I = 4 A

• If three cells with emf 3 V, 2V, and 4V are connected in series, what would be the total emf of the cell. 

Solution: The cell are connected in series therefore total emf would be:

E = E1 + E2 + E3

E = 3 + 2 + 4

E = 9 V

Conclusion 

The resistance is the opposition offered by the wire to the current. The resistance depends on the area of the wire, length and temperature of the wire. There are two possible ways of arrangement of cell and resistance: parallel and series combination. 

The series combination is the one in which cells and resistance are connected from end to end. This kind of arrangement has some drawbacks. The main drawback is that any fault in the circuit can disrupt the complete connection. That is why parallel combinations are preferred.