Voltage And Current Sources: Series And Parallel Connection In Circuits

Series And Parallel Combination Of Current & Voltage Sources

This is my second article on voltage and current sources. The previous article was written on introduction of voltage and current sources and different types of voltage and current sources are discussed. You can view this article here.

Key Questions:

Series connected voltage sources
Under which conditions voltage sources can connect in parallel
Parallel connected current sources
Under which conditions current sources can connect in series

Series Connected Voltage Sources:

Voltage sources should be connected in series. The question is why are voltage sources connected in series?

The answer is more voltage. When voltage sources connected in series with same polarity they will be added.

DC voltage sources connected in series can be combined and replaced with a single equivalent DC voltage source. See Fig 1

AC voltage sources connected in series having same angular frequency can be combined and replaced with a single equivalent AC voltage source. See Fig 1

AC and DC voltage sources connected in series can be combined to get total voltage across them. See Fig 1

Fig 1 Series connected voltage sources

If voltage sources connected in series having same polarity then they are series aiding sources. Since it will add the total voltage. See Fig 2

If voltage sources connected in series with opposite polarity then they are series opposing sources. Since it will decrease the total voltage. See Fig 2

Fig 2 Series aiding and series opposing sources

Parallel Connected Voltage Sources:

Why are voltage sources connected in parallel??

The answer is more current. Let me explain this answer.

Have you seen toys or gadgets in which cells (mistakenly called batteries. Batteries are series connected cells) connected in parallel. Everyone definitely saw these types of gadgets.These cells are connected in parallel to meet the current requirements. To connect voltage sources in parallel each voltage source must have same voltage and polarity and frequency of operation (angular frequency). Under this condition current from each voltage source will be added.

For example 3 AAA size batteries (1.5V) connected in parallel. Voltage remains same in parallel, while the current from each source will be added. And the effective resistance of parallel connected sources would also decrease.

Keep in mind that the parallel connected voltage sources have same magnitude, same polarity and same angular frequency.

Fig 3 Parallel connected voltage sources

Parallel Connected Current Sources:

Current sources should be connected in parallel. The question is why are current sources connected in parallel?

The answer is more current.

According to Kirchhoff's Current Law in parallel connected current sources current will be added.

DC current sources connected in parallel can be combined and replaced with a single equivalent DC current source.

AC current sources connected in parallel and having same angular frequency can be combined and replaced with a single equivalent AC current source.

Fig 4

AC and DC current sources connected in parallel can be combined to get total current flowing across them.

Fig 5

Aiding Sources: If sources are connected in parallel such that all the currents from each source added. For example current sources connected in parallel and with similar polarity.

Opposing Sources: If sources are connected in parallel such that current from different sources are subtract from one another. Example current sources are connected in parallel but with opposite polarity.

Fig 6

Series Connected Current Sources:

Current sources with different current values can not be connected in series. Because it violates Kirchhoff's Current Law (KCL). According to this law current entering the node is equal to current leaving the node. So at a single node two current sources with different current values can not be connected.

For example a current source having 5A and another current source having 1A current are connected in series. Now according to KCL the current entering the node is equal to current leaving the node. But we have 5A current source connected in series with 1A current source. Current from 5A source and current from 1A source are at the same node. Which violates the KCL.

Fig 7

When are current sources connected in series?

Current sources can be connected in series if and only if they carry equal currents.

A 2A current source can be connected in series with 2A current source only. These two current sources can be replaced by single equivalent current source of 2A.

See Fig 7