Let’s Get Physics-l: Kirchhoff’s Second Law

Previously, we had a look at Kirchhoff’s First Law which applies the conservation of charge to electrical circuits. It’s probably best to check it out if you missed it but it’s not essential for this law.

Whilst Kirchhoff’s First Law covered charge, his second covers the conservation of energy within an electrical circuit. It states that, in any closed loop, the sum of e.m.f is equal to the sum of the products of current and resistance (or potential difference).

∑ε = ∑IR or ∑V


  • ε – e.m.f/ V
  • I – Current/ A
  • R – Resistance/ Ω
  • V – Potential difference/ V


My Favourite Armour, very snazzy


If we consider Iron Man’s suit. It’s powered by the Arc Reactor, our battery in this instance, which has an electromotive force. Each repulsor, our components, have current passing through them and consequently have potential differences across them. Now, if we consider Kirchhoff’s Second Law, the sum of these repulsor’s potential differences will be equal to the electromotive force found in the Arc Reactor.


Iron Man’s suit won’t actually operate like this but it helps (I think) convey the idea

Sometimes, circuits have more than one source of e.m.f. It does complicate matters a little bit but not too much. When calculating potential difference, you need to consider the orientation of the cells in a circuit. If they are going the same way then the currents will all be positive (or negative, that’s up to you). However, if they are facing different ways, you need to ensure that you take one way as positive and the other as negative.


  • Kirchhoff’s Second Law – In a closed loop, the sum of the electromotive force is equal to the sums of the products of current and resistance (or potential difference)

With both laws under your belt, working out values for components in a circuit should be a fair bit easier. I will go through some worked examples once we’ve covered all the electricity stuff to reinforce the laws and see how we can apply them. If you have any thoughts or questions please feel free to leave them in the comments. Thank you.

(The Character referenced is property of Marvel Comics and I in now way lay claim to him)






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