Calculating Resultant Voltage in a Series Circuit

When batteries or cells are connected in series, their individual voltages add up to give the total resultant voltage of the combination. This is a fundamental principle in electrical circuits involving power sources.

In this question, we are connecting two Li-Ion cells and one lead acid automobile battery in series. To find the total resultant voltage, we need to know the nominal voltage of each type of battery.

• A typical nominal voltage for a single Li-Ion cell is 3.7 Volts (V).
• A standard lead acid automobile battery is typically a 12 Volt (V) battery.

Since there are two Li-Ion cells connected in series, their combined voltage will be the sum of their individual voltages:

Voltage of two Li-Ion cells in series = Voltage of cell 1 + Voltage of cell 2

Using the nominal voltage of 3.7 V for each Li-Ion cell:

\(V_{2 \times Li-Ion} = 3.7 \, V + 3.7 \, V = 2 \times 3.7 \, V = 7.4 \, V\)

Now, these two series-connected Li-Ion cells are connected in series with the 12 V lead acid automobile battery. The total resultant voltage of the entire combination is the sum of the voltage of the two Li-Ion cells in series and the voltage of the lead acid battery:

Total Resultant Voltage = Voltage of two Li-Ion cells in series + Voltage of lead acid battery

Using the calculated voltage for the Li-Ion cells and the nominal voltage for the lead acid battery:

\(V_{Total} = V_{2 \times Li-Ion} + V_{Lead-Acid}\)

\(V_{Total} = 7.4 \, V + 12 \, V\)

\(V_{Total} = 19.4 \, V\)

Therefore, the resultant voltage generated by a 2-Li-Ion cell connected to one lead acid automobile battery in series is 19.4 V, assuming the nominal voltages for each battery type.

Revision Table: Battery Voltages and Series Connection

Total Resultant Voltage = Voltage of Li-Ion cells in series + Voltage of Lead Acid battery = \(7.4 \, V + 12 \, V = 19.4 \, V\)

Additional Information on Battery Connections and Voltage

Understanding how to connect batteries and the resulting voltage is crucial in many applications. Here's a bit more detail:

• Series Connection: Connecting batteries in series involves connecting the positive terminal of one battery to the negative terminal of the next. This arrangement increases the total voltage while the capacity (Amp-hours) remains the same as that of a single battery. This is useful when you need a higher voltage than a single cell can provide.
• Parallel Connection: Connecting batteries in parallel involves connecting all the positive terminals together and all the negative terminals together. This arrangement increases the total capacity (Amp-hours) while the voltage remains the same as that of a single battery (assuming all batteries have the same voltage). This is useful when you need a longer runtime.
• Nominal Voltage vs. Actual Voltage: The nominal voltage is a standard reference voltage for a battery type. The actual voltage of a battery varies depending on its state of charge and the current being drawn from it. A fully charged battery will have a voltage slightly higher than its nominal voltage, and the voltage will decrease as it discharges. For calculations in problems like this, the nominal voltage is usually used unless specified otherwise.
• Battery Management Systems (BMS): When combining different types of batteries or multiple cells of the same type, especially Li-Ion, a Battery Management System is often used. A BMS helps in monitoring and managing the charging, discharging, and balancing of cells to ensure safety and optimal performance.

In this specific problem, the series connection of batteries leads to the voltages adding up, resulting in a total voltage of 19.4 V based on standard nominal voltages.