There is another way of looking at it. Circuits analysis calls things like this a over-defined circuit. In the real world these circuits don't happen but can happen in diagrams with ideal components.

You don't even need magnetic fields to create such a circuit. Lets go break Kirchhoffs law again!

For example this is an over-defined circuit:

What is the voltage across A and B? Well looking from one side its 1V, looking from the other side is 2V. And look Kirchhoffs voltage law is wrong again! The voltages don't add up anymore.

What happens if you do this in real life? You just get lots of current and the 1V that Kirchhoffs is missing to make it work is in the internal resistances of the voltage sources and wires. This is essentially a battery charger circuit.

Okay okay everyone knows you can't just parallel together voltage sources or series together current sources. That's like dividing by zero in math. So lets take a different circuit then:

When the switch is open its pretty easy to solve the voltages everywhere. A to B is 1V and C to D is 0V (Assuming the capacitor was not given any energy upon its creation in the universe). But then lets close the switch and ask what are the voltages at that moment.

So lets look at it from the left side first:

Voltage source is putting 1V there so A to B must be 1V. And switch is closed so A=C and B=D. So in that case the voltage between C and D is also 1V. Solved

Now lets try solving it from the right side:

If we know the voltage across the capacitor then we can know the voltage between C and D. We do have a formula for the voltage on a capacitor:

So the 1/C part is simple, we know its 1uF so that works out to 1e6. We also know V(t

_{0}) is 0V. All we need is the integral of the current. Since the switch has been closed for 0 seconds means the integral is also 0 so from this we conclude the voltage on C and D is 0V....wait didn't we say it was 1V before?Aha! Dr. Lewin is on to something, it does matter from what direction you look at it!

Alright fine the switch basically didn't do anything because no time has passed. Lets fix out question a bit then "What is the average voltage on the nodes in the span of 1ms of the switch closing". Okay now we are integrating from t=0 to t=0.001 .This time we do need to calculate the current, since this is one loop this is easy. We just sum up all the voltages and resistances and use Ohms law. So we get I = 1V / 0 Ohm ... yeah we can't divide by zero so the current is undefined. So the integral is undefined. So the voltage on C and D is also undefined. Okay fine we could say the current is infinite since approaching division by zero limits towards infinity. Well then the integral is also infinite and we find C and D have infinitely large voltage. But as soon as we introduce a resistance of not 0 in there we can calculate it just fine and it becomes a mathematically valid circuit.

This is the same as trying to solve:

x^{2} = -3

x = ?

Yes i know this has a complex number answer, but when doing DC circuit analysis what does a current of 2+j3 Amps look like in DC?Circuit analysis methods break when you introduce these over-defined circuits, its not just SPICE that will throw a angry error message at you for trying to simulate one. Analyzing it by hand simply gives you weird results like 0, undefined or infinity in places where there should be a sensible number, or you get multiple results for the same voltage or current depending on what path you calculate.

Dr. Lewins circuit is also such a circuit because he is forcing a current around while the resistors try to define there own current. Its not only Kirchhoffs law that breaks in such circuits, you can break many other laws since the math simply does not come together.