# Two Parallel Voltage sources and KVL

• ecy5maa
In summary: If you add a wire between the two, you have a loop which would have a voltage of 5V. However, this contradicts the fact that the two sources should be equal, resulting in mathematical inconsistencies. It also has practical implications, such as one battery charging the other or the wire heating up.
ecy5maa
Hi,

I understand that you cannot apply KVL to voltage sources connected in parallel, unless both voltage sources are the same, as this violates KVL.

However, I want to know why? Just a simple 2-3 line explanation will suffice.

Regards

From a KVL point of view, if you summed up the voltages around the loop, they wouldn't add up to zero.

From a practical point of view, you'll have one battery charging the other (assuming the polarities were correct, and the voltages were appropriate), or, if they were severely mismatched, one (if not both) would probably blow up. That or the wire connecting them would get really, really hot (acting as a low resistance resistor).

EDIT: I should clarify that when you go around the loop and take account of all the voltages, you have to set that to zero, which leads to mathematical inconsistencies as sophiecentaur mentions below. For instance, write out the KVL equation for a 2V supply in parallel with a 3V supply, such that like terminals are connected together (+ with +, - with -).

Last edited:
ecy5maa said:
Hi,

I understand that you cannot apply KVL to voltage sources connected in parallel, unless both voltage sources are the same, as this violates KVL.

However, I want to know why? Just a simple 2-3 line explanation will suffice.

Regards

A voltage source is a fixed value, whatever the load. Modelling the effect of connecting two in parallel would be like trying to do maths but saying 3=2.

## 1. What are two parallel voltage sources?

Two parallel voltage sources are two independent sources of electrical energy that are connected in parallel to a circuit. This means that the positive terminals of the two sources are connected together, as well as the negative terminals.

## 2. Why is Kirchhoff's Voltage Law (KVL) important when dealing with two parallel voltage sources?

Kirchhoff's Voltage Law is important because it states that the algebraic sum of all voltages around a closed loop in a circuit must equal zero. In the case of two parallel voltage sources, KVL ensures that the voltages from each source do not conflict with each other and that the total voltage in the circuit is consistent.

## 3. How do you apply KVL to a circuit with two parallel voltage sources?

To apply KVL to a circuit with two parallel voltage sources, you must first choose a direction for the current flow. Then, you can write an equation using KVL that states that the sum of the voltage drops in the loop must equal the sum of the voltage sources. This equation can then be solved for the unknown currents in the circuit.

## 4. Can two parallel voltage sources have different voltages?

Yes, two parallel voltage sources can have different voltages. In fact, this is often the case in real-world circuits where multiple sources of electrical energy are connected together. As long as the voltages are not in direct conflict with each other (i.e. one source is trying to push current in the opposite direction of the other), the circuit will function properly.

## 5. What happens if the two parallel voltage sources have the same voltage?

If the two parallel voltage sources have the same voltage, then the circuit will behave as if there is only one voltage source. This is because the two sources will essentially cancel each other out and there will be no difference in potential between the two points where they are connected in parallel. However, this scenario is uncommon and can lead to unnecessary complications in circuit analysis.

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