Cells in Series and Parallel for IIT JEE

Series and Parallel Circuits

The most commonly used methods for the connection of electrical parts are parallel connection and series connection. To understand about the functioning of cells in both these types of connections, it is important to first understand what a cell is. The cell forms a significant important aspect of any electric circuit. Let us now know more about cells, parallel connection and series connection. 


A cell produces electricity. It also derives chemical reactions. A common example of cells is electrochemical cells, also called as batteries. There are two terminals in each and every cell. 

Anode: It is the terminal of the cell from which the current enters and leaves the electrical circuit. In other words, Anode is the terminal of the cell that serves as an incoming source for the entrance and exit of current to and from the device.

Cathode: It is the terminal of the cell that serves as an outgoing channel for the current to flow outside the device or the circuit.
Now after learning about the two terminals of the cell, we will now understand the ways in which cells are connected to form a circuit. There are mainly two ways in which cells are connected to each other. These are series connection and the parallel connection. 

Series Connection: 

In the series connection, components are connected in a sequential set of components. Here the cells are connected from end to end such that the same amounts of current passes through each and every cell in the circuit. 

When the cells get connected in series, then the battery emf is joined to the total of the electro motive force of the individual cells. Now let us suppose that there are several cells arranged in a way that the positive end of first cell is joined to the negative end of the first cell and the negative end of the second terminal is connected to the positive end of the second cell and so on. This type of arrangement shows that all these cells are joined in series.

Resistance of Cells or Equivalent EMF when cells are joined in series

Now once we have understood in what fashion cells are arranged in a series connection, we will now move to calculating EMF of the cells in this type of connection. If “E” is denoted as the overall electromotive force of the battery along with n number cells, and “E1”, “E2 , “E3” , “En” be the electromotive force of individual cells, then 

E= E1 + E2 + E3 + …….En

In the same way if r1, r2, r3, rn be the internal resistances of cells, then the combined internal resistance of a battery is equivalent to the total of internal resistances of individual cells. This can be shown in the form of the below equation:

R= r1 + r2+ r3 + ….. rn

Parallel Connection: 

Parallel connection is denoted as the connectivity of the parts of the electrical circuit alongside the other parts. In cells that are in parallel connection, the amount of current gets divided among the different cells. 

In case of a parallel cell combination, all the (-) ends of the cell are joined and all the (+) end are joined. This forms the parallel connection. Now let us see how to calculate the internal resistance or electromotive force of cells in this type of connection.
If electromotive force of each cell is the same, then the battery emf combined with “n” numbers of cells when connected in a parallel connection is equivalent to the electromotive force of each and every cell. The resultant value of internal resistance of this entire combination is,

r = (1r1 + 1r2 + 1r3 +… 1rn)-1

Resistance of Cells or Equivalent EMF in parallel and series

Suppose that the electromotive force of each cell is denoted as “E” and internal resistance of cells is denoted by “r”. As cells are connected in a series combination, the emf of each cell and the battery will be denoted as nE. The “equivalent resistance”will be denoted as nr. In case, when series of cells is combined in parallel connection, then the equivalent internal resistance for that series will be given as is nr/m.

So how does a series connection of cell differ from the parallel connection of cells?

The primary difference between a parallel circuit and a series circuit is that all of its components in a series connection share the same amount of current whereas in the case of a parallel connection, all the components have the same amount of potential difference in between them.

Components that are joined in series along one path have the same amount of current flowing through the different components of the circuit. Components that are connected in a parallel connection are connected along various paths and witness the same amount of voltage applied to each and every component in that circuit.

In case of a parallel circuit, there are various paths for the flow of current in the circuit. In this case, the total value of current that flows through the cells remains the same when compared to each individual cell. 

In case of two 1.5 V cells connected in the parallel connection, the voltage received by each load remains the same, but the power gets increased. This implies that the battery life also increases and it lasts for a longer time.

In any circuit, a cell is something that pushes to make the current flow through it. This leads to the formation of potential difference in the circuit. When cells get connected in a series combination, their voltages get added up. 

So, if two cells of 1.5 volts are connected in series then the total voltage provided by them would be three volts, whereas it is when three cells are connected in series, then the total voltage is 4.5 V. Generally, series combination of cells is used in those types of equipment where higher voltages are required. So to generate higher voltages, it is important to join the cells in a series combination.

Parallel and series configurations of resistor have got very different types of electrical properties in them. In case of a pure parallel circuit, you will never find more than 2 pairs of electrically common points, irrespective of the number of components connected in the circuit. There can be several paths for electrons to pass, but just a single voltage present across all components. 

Parallel circuits have got multiple branching pathways that make the electrical current flow through them whereas in case of a series circuit it forms one path. The components of any parallel circuit get connected in a different way, than they are connected in a series circuit. The entire form of the arrangement impacts the magnitude of current that passes through the circuit.

On joining two same types of batteries in a parallel connection, it is observed that the output capacity gets doubled while the output voltage remains the same. In the second case, if you find that 2 similar batteries get connected in a series combination, then the output voltage gets doubled whereas the output capacity remains the same. 

What makes the resistance of a series circuit different from the resistance of a parallelcircuit?

The total resistance in a circuit where the resistors are joined in a series combination is the total of the individual resistances. Each of the resistors connected in a parallel combination has got the same full voltage as applied by the source. The current that flows through each of the resistors present in a parallel combination varies on the basis of the resistance.

Why is that the voltage is measured as same in a parallel combination of cells?

In a parallel combination of cells, the amount of difference in the electric potential across the different resistors is the same. In case of a parallel circuit, the reduction in the voltage across the different branches remains the same as the gain in the battery voltage. Thus, the drop in the voltage is measured to be same across all the resistors.

Why does the current remain the same in a series combination of cells?

In a series connection, the current that flows through each resistor is the same. In case of an identical light bulb, the amount of resistance is the same for each resistor. The increase in the voltage in the battery has to be identical as the sum of voltage reductions across these resistors.

In what ways does series resonance differs from parallel resonance?

The major difference between any parallel and series resonance is that in case of a series resonance, the arrangement of all the circuit components forms the minimum impedance. On the other hand, in case of a parallel resonance, the arrangement of component forms the largest impedance.

Which is more efficient a parallel circuit or a series circuit?

Parallel circuits are considered to be more useful because when one of the circuits goes out, there are a few more circuits that can run the appliance which is not the case in series combination where there is only one circuit.

Why the resistance is higher in series combination?

As in a series connection, the current has to flow through all the connected resistors; it causes the resistance to increase. This is not the case in parallel combination.