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A short class with Sarah and her students. The other ways are under More.
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Today, we're going to talk about how cells can be connected in series. Who can tell me what happens to the total voltage when cells are in series?
The total voltage increases!
Correct! When you connect cells in series, their voltages add up. If we have two cells with emfs of e₁ and e₂, the total emf, e_eq, becomes e₁ + e₂. Can anyone memorize that?
Uh, would it be 'E equals e₁ plus e₂'?
Exactly! You can think of it as 'Every cell adds energy!' Remember the acronym E^2 for Double Energy. Now, what about the internal resistance?
Does it add up too?
Yes, it does! The equivalent internal resistance, r_eq, is equal to r₁ + r₂. So, more cells mean a higher total resistance. Can you see the importance of both total voltage and resistance?
Yes! If I have more cells in series, I have more voltage but also more resistance.
Right! In summary, when cells are in series, the equation for total voltage and internal resistance is crucial for understanding how to manage power in a circuit.
Now, let's shift our focus to parallel connections of cells. What remains the same in a parallel combination?
The voltage stays the same!
Yes! In a parallel connection, the voltage across all cells is equal to the voltage of one of the cells. In other words, e_eq equals e₁ if all cells have identical emfs. But what happens to the current capacity?
The current increases, right?
Exactly! The total current is the sum of the currents from each cell. So if the cell currents are I₁ and I₂, the total current, I_eq, is I₁ + I₂. Would anyone like to remember this by creating another acronym?
Maybe we could use C for Current? So 'C equals I₁ plus I₂'?
Great suggestion! 【C = I₁ + I₂】 helps remember that combining cells in parallel increases the total current. However, how do we calculate the equivalent internal resistance?
Is it just like in series?
Not quite! It's actually the inverse: 1/r_eq = 1/r₁ + 1/r₂. This means that adding more cells decreases the overall resistance. Why is this beneficial?
It allows more current to flow without increasing the voltage!
Exactly! That’s why parallel arrangements are often used to achieve higher current capabilities while keeping the voltage consistent.
Let's discuss where we might see series and parallel arrangements of cells in real life. Can anyone think of an example?
A flashlight uses batteries in series, right?
Correct! This setup gives it a stronger light because the voltage is higher. What about parallel arrangements?
Like in cars, where batteries can be in parallel to ensure the power supply can sustain more load?
Exactly! Cars often have multiple batteries in parallel to provide extra current when needed, like during starting. What do you think the disadvantage would be for a series connection?
If one battery dies, it won't work.
Right! In series, if one cell fails, the whole system fails. In contrast, in a parallel configuration, the failure of one cell does not affect the current supply from the other cells. That's the power of configuration.
In series they add, stacking up high, voltage is increasing, oh my oh my!
Imagine a string of pearls where each pearl represents a battery in series, creating a long, bright necklace of energy.
For cell Sequence, remember V = V1 + V2 for Series, while for Parallel, I = I1 + I2.
In series, Summate the voltage to get Strength.
Term
What happens to voltage in cells in series?
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Term
What happens to current in cells in parallel?
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The energy provided per unit charge by a source of electrical energy, measured in volts.
The resistance within a battery or cell that causes a drop in potential when current flows.
The total resistance of a combination of resistors or cells in a circuit.
A configuration where components are connected end-to-end, resulting in the same current flowing through each.
A configuration where components are connected across common points, allowing for multiple paths for current.
This section discusses how cells (batteries) can be arranged in series and parallel configurations in electric circuits, detailing their effects on voltage and internal resistance.
Understanding the arrangement of cells in series and parallel is vital for circuit design. Cells in series increase the total voltage while maintaining the same current, while parallel arrangements keep the voltage constant but increase the total current capacity. The internal resistances also combine differently in these configurations, affecting the overall circuit performance.
In electric circuits, cells can be arranged in two main configurations: series and parallel. In a series configuration, the positive terminal of one cell is connected to the negative terminal of the next cell, resulting in the total electromotive force (emf) being the sum of the individual emfs of the cells. If the cells are denoted by their emfs as e₁ and e₂ and their internal resistances as r₁ and r₂, the combined emf and internal resistance of the configuration can be expressed as:
Equivalent emf in series:
e_eq = e₁ + e₂
Equivalent internal resistance in series:
r_eq = r₁ + r₂
In contrast, when cells are arranged in parallel, each cell connects to the same two points in the circuit. This setup keeps the voltage the same as that of a single cell but increases the total available current capacity. For parallel configurations, the equations are:
Equivalent emf in parallel:
e_eq = e₁ = e₂ (if they are identical)
Equivalent internal resistance in parallel:
1/r_eq = 1/r₁ + 1/r₂
These configurations allow for enhanced flexibility in circuit design, leading to efficient utilization of battery power according to the requirements of various electrical devices.