Why Does Kirchoff's Second Law State That Voltages in a Closed Loop Sum to Zero?

[princejan7]

http://postimg.org/image/ubkhk78fn/

Can someone explain why "the sum of the voltages equals zero for any closed path in an electrical circuit"?
(an explanation in terms of electric potential, polarity, resistors etc. and not a water analogy or anything like that)

 

[Simon Bridge]

Law of conservation of energy.

 

[lightgrav]

voltage is a difference in potentials at two places; let's presume that charge is slow enough that we can treat things as almost static (that is, magnetic fields are changing slowly!).
This means (calling the electric potential V = PE/q) that the "voltage across R1" for example, is V32 = V3 - V2.
(suggestion: if you NUMBER your devices, you should LETTER your locations; I will bold locations)
The voltage across R2 is V43 = V4 - V3 .
What is the voltage across the pair (R1 + R2)? it is V4 - V2 , from starting place 2 to ending place 4. do you get the notation? it is about place difference.

So, what is the voltage across the entire loop, from battery bottom (1) around to battery bottom (1) ... it is It is apparently V11 = V1 - V1 = 0
(cause anything - itself =0)

 

[CWatters]

Consider this circuit which is yours with the loop broken...

Voltages in series add so...

V₁₅ = V₁₂ + V₂₃ + V₃₄ + V₄₅

If you then connect node 5 to node 1 ...

V₁₅ = V₁₁

Clearly V₁₁ must be zero because it's the voltage measured between node 1 and node 1 which is the same place.

So with the loop completed..

V₁₂ + V₂₃ + V₃₄ + V₄₅ = V₁₅ = V₁₁ = 0

 

[HalfLostAndSearching]

Kirchoff's second law, also known as the voltage law, states that the algebraic sum of the voltage drops around any closed loop in an electrical circuit is equal to zero. This means that the sum of all the voltage sources in the circuit is equal to the sum of all the voltage drops across the circuit's resistors.

To understand this law, we need to first understand the concept of electric potential. Electric potential is a measure of the potential energy per unit of charge at a certain point in the circuit. It is measured in volts (V). In a closed circuit, the electric potential remains constant throughout, but it can vary at different points in the circuit.

In a circuit, voltage sources, such as batteries or generators, provide a certain amount of electric potential to the circuit. This electric potential is then used up or "dropped" as the current flows through the circuit's resistors. Resistors are components that resist the flow of current and cause a voltage drop across them. This voltage drop is proportional to the amount of resistance in the circuit.

Now, according to Kirchoff's second law, the sum of all the voltage drops across the resistors must equal the sum of all the voltage sources in the circuit. This is because in a closed loop, the current flows in a continuous path, starting and ending at the same point. Therefore, the amount of electric potential gained from the voltage sources must be equal to the amount of potential lost or dropped across the resistors.

In other words, the voltage sources provide the energy to push the current through the circuit, while the resistors consume this energy and cause a voltage drop. The total amount of energy provided by the voltage sources must be equal to the total amount of energy consumed by the resistors, as per the conservation of energy law.

In summary, Kirchoff's second law is a fundamental principle in electrical circuits that ensures the conservation of energy. It states that in a closed loop, the sum of all the voltage drops must be equal to the sum of all the voltage sources, which is essential for the proper functioning of an electrical circuit.