Reference Potential in AC circuits

Question

In DC circuits, we are free to choose ANY point (let's call it point P) and elect its electric potential to be 0 V. That point becomes the reference voltage point so that all other points in the circuit have a potential $V$ that is either zero, positive or negative. Practically speaking, with the black lead of a voltmeter touching P, we can measure the potential of any other point with the red lead. Additionally, in DC, the 0 V point belongs to a wire and all points on that wire are equipotential and have "0"V. So the reference is not just a point but an entire conductor (wire, plane, etc.) where all points have 0 V.

In the AC case (low frequency), the electric potential of the points in the circuit is changing in time. For example, consider a sinusoidal source connected to a resistor. Given that the potential at any chosen point changes with time, do we just pick any arbitrary physical point, like we do in DC circuit and, and assign to it the 0 V even if we know that its potential is constantly changing?

If the frequency is very high and the wires are long enough, we need to consider transmission line effect. The potential at different points on the same wire on each side of the resistor will have different potentials V.... Isn't it a problem when we try to select the reference point with 0 V in that case? We could pick a point to be the 0V but all other points on the same conductor would have varying potentials not equal to 0V if measured with a voltmeter...

Thanks!

Answer 1

In the AC case (low frequency), the electric potential of the points in the circuit is changing in time. For example, consider a sinusoidal source connected to a resistor. Given that the potential at any chosen point changes with time, do we just pick any arbitrary physical point, like we do in DC circuit and, and assign to it the 0 V even if we know that its potential is constantly changing?

You can choose any point to be referenced 0V potential. In AC what will change is the potential of other points of the circuit.

Answer 2

If the frequency is very high and the wires are long enough, we need to consider transmission line effect.

When working with high frequency signals, transmission line effects should be analyzed for any length of conductor, not only "long" lines.

The potential at different points on the same wire on each side of the resistor will have different potentials V.... Isn't it a problem when we try to select the reference point with 0 V in that case?

Don't forget that voltage is nothing more than the difference of two potentials,

$$ V = P_2 - P_1 $$

where \$P_1\$ is the reference potential, and the reference potential can be any potential \$P_x\$. And of course, each time you chose a different reference potential value \$P_1\$—i.e., if probe \$P_2\$ is not moved, but probe \$P_1\$ is moved to a different node within a circuit—the measured voltage \$V\$ changes. Likewise, if probe \$P_1\$ is not moved (the reference potential remains constant) and probe \$P_2\$ is moved to a different node, the measured voltage changes.

We could pick a point to be the 0V but all other points on the same conductor would have varying potentials not equal to 0V if measured with a voltmeter...

In a real transmission line, this is more-or-less what we observe when a time-varying signal is injected into the line, i.e., at time \$t\$ we observe different voltages at different locations along the line relative to the chosen reference potential. And of course, changing the location of the reference potential changes the measured voltages along the transmission line.

[NOTE: A typical voltmeter is not particularly useful for making voltage measurements along a transmission line. One typically uses a high-speed oscilloscope, or a slotted line setup, etc. — end note]