Why does a resistor that isn't connected to anything in one of its terminals has a null current?

Question

For example, in the following circuit:

The $2Omega$ resistor is "floating" since it's not connected to anything in its right terminal. Hence, $i_1=0$. I've seen that one of the requirements for a current to flow around a path is to have a voltage difference, and since we don't have any voltage on the right terminal of the resistance, I'm assuming that's why $i_1=0$; but I'd like to have a better insight of why does that happens.
Thanks in advance.

Bob D · Accepted Answer

A water pipe analogy might help.
Let the 2 Ohm resistor be the length of a water pipe. At the end of the pipe is a shut off valve. This prevents water from flowing through the pipe. If water could flow, there would be a drop in pressure between beginning and end of the pipe, like a voltage drop across the resistor due to current flow and ohms law.
But if the pipe is closed off at the right end (a closed switch in the circuit) water can't flow, and a pressure gauge located at the end of the pipe would read the same pressure as a gauge at the beginning of the pipe, or $Delta P=0$. The electrical analogue is current can't flow so a voltmeter connected across the open 2 Ohm resistor will read zero voltage because the potential is the same on both ends of the resistor, or $Delta V=0$.
Hope this helps.

Solomon Slow · Answer

I'm not sure I 100% understand your question, but you seem to be asking, why is $i_1=0$. Is that right?
One answer is to invoke Kirchoff's Current Law (KCL): The sum of currents entering any one node must equal zero. Well, there's only one way in to that node. If the sum of one thing must equal zero, then that thing itself must be zero.

Why does a resistor that isn't connected to anything in one of its terminals has a null current?

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