Understanding Parallel Connection of Voltage Sources

The question asks about the output voltage when multiple identical voltage sources, specifically six 12 V cells, are connected in parallel. Understanding how voltage sources behave in different configurations like series and parallel is fundamental in electrical circuits.

When electrical components, including voltage sources like cells or batteries, are connected in parallel, they are placed across each other such that the positive terminals are connected together, and the negative terminals are connected together. This creates multiple paths for the current to flow.

Output Voltage in Parallel Connection of Identical Cells

A key principle for parallel connection applies when the voltage sources are identical (having the same voltage rating and internal resistance). In such a case, the total voltage across the parallel combination is equal to the voltage of a single source. This setup does not increase the voltage, but it increases the total current capacity (often measured in Amp-hours or Ah) available from the combination. This is because the load current is shared among the parallel sources.

Mathematically, for 'n' identical cells, each with voltage \(V_{cell}\), connected in parallel, the total voltage \(V_{total}\) is given by:

\[ V_{total} = V_{cell} \]

In contrast, if these cells were connected in series, their voltages would add up. For 'n' identical cells each with voltage \(V_{cell}\) connected in series, the total voltage \(V_{total}\) would be:

\[ V_{total} = n \times V_{cell} \]

Calculating Output Voltage for Six 12 V Cells in Parallel

We are given six identical cells, each with a voltage of 12 V, connected in parallel. Applying the rule for identical voltage sources in parallel:

• Number of cells, \(n = 6\)
• Voltage of each cell, \(V_{cell} = 12 \, \text{V}\)
• Connection type: Parallel

Using the formula \(V_{total} = V_{cell}\) for parallel connection of identical sources:

\[ V_{total} = 12 \, \text{V} \]

Therefore, the output voltage across the parallel combination of six 12 V cells is 12 V.

Comparing with Series Connection

Just to illustrate the difference, if these six 12 V cells were connected in series, the output voltage would be:

\[ V_{total\_series} = 6 \times 12 \, \text{V} = 72 \, \text{V} \]

This clearly shows that parallel connection maintains the voltage, while series connection increases it.

Based on the analysis, connecting six 12 V cells in parallel results in an output voltage of 12 V.

Revision Table: Parallel and Series Cell Connections

Additional Information: Cell and Battery Configurations

Cells are the basic units that store chemical energy and convert it into electrical energy. A battery is typically made up of one or more cells. Connecting cells in series or parallel allows us to achieve desired voltage and current ratings for various applications.

• Series Connection: Used to increase the total voltage. The current rating remains the same as that of the lowest-rated cell in the series (ideally, cells are identical). If one cell fails in series, the entire circuit might break (open circuit).
• Parallel Connection: Used to increase the total current capacity. The voltage remains the same (if identical cells). If one cell fails in parallel (e.g., becomes an open circuit), the others can still supply current, although the total capacity is reduced. If a cell fails as a short circuit, it can be dangerous and potentially damage other cells or the circuit.
• Series-Parallel Connection: A combination of both, used to achieve both a higher voltage and a higher current capacity. For example, you could connect groups of cells in series, and then connect these series groups in parallel.

Understanding these fundamental configurations is crucial for designing and working with battery packs for various devices, from small electronics to electric vehicles.