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