Cells and cell combinations
Cells and Cell Combinations
Cells are the basic building blocks of life in biology, but in the context of physics and specifically current electricity, a cell refers to a device that converts chemical energy into electrical energy. Cells can be combined in various ways to increase the voltage or current output, which is essential for powering electrical devices. In this article, we will explore the different types of cells and how they can be combined to meet specific electrical requirements.
Types of Cells
There are two main types of cells used in electrical circuits:
Primary Cells: These are cells that cannot be recharged once they are depleted. They are used until the chemical reactions within the cell exhaust the chemicals that produce electricity. Examples include the alkaline battery and the zinc-carbon battery.
Secondary Cells: These are rechargeable cells that can be used multiple times. They can be recharged by applying an external electrical current, which reverses the chemical reactions that occur during discharge. Examples include lithium-ion batteries and lead-acid batteries.
Cell Combinations
Cells can be combined in two fundamental ways:
Series Combination: Cells are connected end to end, with the positive terminal of one cell connected to the negative terminal of the next cell. This increases the total voltage of the combination.
Parallel Combination: Cells are connected with all positive terminals connected together and all negative terminals connected together. This increases the total current capacity without increasing the voltage.
Series Combination
In a series combination, the total voltage $(V_total)$ is the sum of the individual cell voltages $(V_1, V_2, ..., V_n)$. The total resistance $(R_total)$ is the sum of the internal resistances $(r_1, r_2, ..., r_n)$ of the cells plus the external resistance $(R_ext)$ of the circuit.
The total voltage in a series combination is given by:
$$ V_{\text{total}} = V_1 + V_2 + \ldots + V_n $$
The total current (I) flowing through the circuit can be calculated using Ohm's law:
$$ I = \frac{V_{\text{total}}}{R_{\text{total}}} $$
where
$$ R_{\text{total}} = r_1 + r_2 + \ldots + r_n + R_{\text{ext}} $$
Parallel Combination
In a parallel combination, the total voltage $(V_total)$ is equal to the voltage of each individual cell (assuming they are identical), and the total current capacity is the sum of the individual cell currents $(I_1, I_2, ..., I_n)$.
The total current in a parallel combination is given by:
$$ I_{\text{total}} = I_1 + I_2 + \ldots + I_n $$
The total effective resistance $(R_eff)$ can be calculated using the formula for parallel resistances:
$$ \frac{1}{R_{\text{eff}}} = \frac{1}{r_1} + \frac{1}{r_2} + \ldots + \frac{1}{r_n} + \frac{1}{R_{\text{ext}}} $$
Differences Between Series and Parallel Combinations
Here is a table summarizing the differences between series and parallel combinations of cells:
| Feature | Series Combination | Parallel Combination |
|---|---|---|
| Voltage | Increases | Remains the same |
| Current | Remains the same | Increases |
| Formula for Total Voltage | $V_{\text{total}} = V_1 + V_2 + \ldots + V_n$ | $V_{\text{total}} = V$ (for identical cells) |
| Formula for Total Current | $I = \frac{V_{\text{total}}}{R_{\text{total}}}$ | $I_{\text{total}} = I_1 + I_2 + \ldots + I_n$ |
| Internal Resistance | $R_{\text{total}} = r_1 + r_2 + \ldots + r_n + R_{\text{ext}}$ | $\frac{1}{R_{\text{eff}}} = \frac{1}{r_1} + \frac{1}{r_2} + \ldots + \frac{1}{r_n} + \frac{1}{R_{\text{ext}}}$ |
Examples
Example 1: Series Combination
Suppose we have three cells, each with a voltage of 1.5 V and an internal resistance of 0.5 Ω, connected in series to a circuit with an external resistance of 5 Ω. The total voltage is:
$$ V_{\text{total}} = 1.5\,V + 1.5\,V + 1.5\,V = 4.5\,V $$
The total resistance is:
$$ R_{\text{total}} = 0.5\,Ω + 0.5\,Ω + 0.5\,Ω + 5\,Ω = 7\,Ω $$
The total current flowing through the circuit is:
$$ I = \frac{4.5\,V}{7\,Ω} \approx 0.643\,A $$
Example 2: Parallel Combination
Now, let's consider the same three cells connected in parallel to the same external resistance of 5 Ω. The total voltage remains the same as the voltage of one cell:
$$ V_{\text{total}} = 1.5\,V $$
The effective resistance is calculated as:
$$ \frac{1}{R_{\text{eff}}} = \frac{1}{0.5\,Ω} + \frac{1}{0.5\,Ω} + \frac{1}{0.5\,Ω} + \frac{1}{5\,Ω} $$
$$ R_{\text{eff}} \approx 0.455\,Ω $$
The total current capacity is:
$$ I_{\text{total}} = \frac{1.5\,V}{0.455\,Ω} \approx 3.297\,A $$
In conclusion, understanding how cells and their combinations work is crucial for designing circuits that meet specific voltage and current requirements. The choice between series and parallel combinations depends on whether an increase in voltage or current is needed for the application.