What Happens When You Connect Different Voltage Batteries in Parallel?

In summary: This is called a trivial solution, because it's the only solution that's possible. But real world electrical components usually don't have this property.
  • #1
Amaterasu21
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Hi all,
I've been thinking about a hypothetical circuit with (say) a 6V cell of negligible internal resistance, a 4V cell of negligible internal resistance, and a resistor in parallel with each other, and I can't figure out what the potential difference across the resistor would be. I've tried to apply Kirchoff's voltage rule about the emfs and p.d.s around a closed loop, but I can't see how to apply it without contradictory answers. Any help?

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  • #2
The circuit theory assumptions have to break down for this circuit, for if the wires are truly resistance-free then KVL applied around the upper loop implies ##6-4 = 0##. There must be some impedance lumped with the cells (be it in the wires or the cells themselves).
 
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  • #3
Amaterasu21 said:
I can't see how to apply it without contradictory answers.
That is correct. It is a self contradictory scenario and therefore all you can get is contradictory answers.
 
  • #4
You can conceive of several other contradictions leading to seeming paradoxes.

For example, a short circuit across an ideal voltage source. Or an open circuited ideal current source.

They can all be resolved by remembering that valid circuit analysis should never result in infinite voltage or infinite currents. If your scenario leads to such an infinity, then circuit analysis rules do not apply.
 
  • #5
Amaterasu21 said:
... a 6V cell of negligible internal resistance, a 4V cell of negligible internal resistance, and a resistor in parallel with each other, ...
That circuit definition contains a KVL contradiction.
You must specify the internal resistance of both cells before solving the circuit.
 
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  • #6
An important point to remember here is that Kirchoff's Voltage and Current laws are only applicable for circuit analysis. Circuit analysis is a highly abstract method of modelling the real world using ideal components. These are generally restricted to resistors, capacitors, inductors, voltage sources, and current sources (there are a few others that you rarely see). These aren't the same as real voltage sources, inductors, etc. Think of it as a graphical version of simple mathematical equations. One consequence of this is that you can construct circuits that don't make sense. Like a 4V battery in parallel with a 6V battery. This is equivalent to the algebraic problem x=4 and x=6, find the value of x.

So, for real world electrical components we will use these simple ideal circuit elements to model the real component as a small network. For example, batteries may be shown as a voltage source with one (or more) resistors. How you choose to model your components allows you to decide how accurate (and difficult) your solutions are.

There are a lot of really well educated people that don't understand this. Including a rather famous MIT physics professor. It's not that they don't know physics, it's that they don't know how EEs talk about network analysis with "lumped element" models (also, they may not know about the problems with voltage and/or current probes in the lab).

If you study network theory, you'll learn of two subtle, but impossible scenarios*. The first is any circuit loop that includes only voltage sources and/or capacitors. The second is any circuit node that only has current sources and/or inductors connected to it. Your network has the former.

* There is a trivial solution where all of the initial conditions match perfectly.
 
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FAQ: What Happens When You Connect Different Voltage Batteries in Parallel?

How do I determine the voltage of each component in a circuit?

To determine the voltage of each component in a circuit, you can use Ohm's Law (V=IR) and Kirchhoff's Voltage Law (KVL). Ohm's Law states that the voltage (V) equals the current (I) multiplied by the resistance (R). KVL states that the sum of all voltages in a closed loop of a circuit is equal to zero. By using these laws and analyzing the circuit, you can solve for the voltage of each component.

What is the purpose of a circuit diagram?

A circuit diagram is a visual representation of an electrical circuit. It is used to show the components and connections in a circuit, making it easier to understand and analyze. It also allows for easier troubleshooting and designing of circuits.

How do I calculate the total resistance in a series or parallel circuit?

In a series circuit, the total resistance is equal to the sum of all individual resistances. So, to calculate the total resistance, you simply add up all the resistances in the circuit. In a parallel circuit, the total resistance is calculated using the formula 1/Rtotal = 1/R1 + 1/R2 + ... + 1/Rn, where R1, R2, etc. are the individual resistances. Once you have the total resistance, you can use Ohm's Law to calculate the current and voltage in the circuit.

What is the difference between a series and parallel circuit?

In a series circuit, the components are connected in a single loop, meaning the current has only one path to flow through. In a parallel circuit, the components are connected in multiple branches, allowing the current to have multiple paths to flow through. This results in different calculations for total resistance and current in the two types of circuits.

How do I troubleshoot a circuit that is not working?

First, check all connections and make sure they are secure. Then, use a multimeter to test for continuity and voltage at different points in the circuit. If the circuit is still not working, you may need to replace a component or consult a professional for further assistance.

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