# What comes first, Voltage or Current?

Impedance can be defined as cause / effect or Z = E / I.

This means that a difference in voltage potential causes a flow of current, the rate of current flow depending on the impedance.

In a dipole antenna, does this mean the applied RF voltage at the feed point causes the flow of RF current in the antenna ?

https://www.youtube.com/watch?v=DovunOxlY1k

• What exactly do you mean by "cause" and "effect"? Do you really mean "premise" and "conclusion"? Or something else, and if so, what exactly? Jun 5 '21 at 0:35
• Or another approach: can you think of an experiment which would confirm or refute your hypothesis? Jun 5 '21 at 0:35

## 4 Answers

In dynamic systems modeling, this issues is known as causality.

In the case of inductances, one instantaneously asserts a voltage across the inductor and the inductive system then returns a time-varying value for the current. So, voltage is the input and current is the output. Note that it is impossible to instantaneously assert a current through an inductor, as this would require infinite voltage.

In the case of capacitances, one instantaneously asserts a current across the capacitor and the capacitive system then returns a time-varying value for the voltage, so, current is the input and voltage is the output in this case. Note that it is impossible to instantaneously assert a voltage across a capacitor as this would require infinite current.

In both cases, this is known as integral causality and is explained in detail in a treatment of power bond graphs.

In the case of a pure resistance, one can either assert a voltage as the input and obtain a current as the output, or assert a current as the input and obtain a voltage as the output.

For an antenna driven at resonance, the load is purely resistive, and current and voltage are related by ohm's law. If it is driven off-resonance, the load will possess either a capacitive or an inductive component and the above commentary applies.

Voltage and current are coupled by resistance in a passive device. V=IR. However, in an AC circuit, R can be complex, which allows a phase difference between current and voltage. Neglecting that, or looking at average over time, voltage and current are proportionally related, and you can't have one without the other if there is conduction and resistance. Voltage over a resistance induces current. Current over a resistance induces voltage. The only way to have one without the other is to have infinite resistance (voltage without current) or zero resistance (current without voltage).

An antenna has loss resistance and radiation resistance. Current and voltage together over these resistances cause the antenna to radiate (and heat up). (One hopes the loss resistance heating the antenna is much smaller than the radiation resistance causing it to radiate.)

• Thanks for the answer, in the case you mention where current over a resistance induces a voltage, what causes that current to flow ? May 29 '21 at 23:07
• Why does anything have to "cause" the current to flow? Maybe it just exists. In a superconductor, that's certainly true. If there's resistance involved, there must be an external force (e.g., a power supply) to replace the energy dissipated by the resistance. In this case, it is the radio. May 30 '21 at 13:27

In a transmitter with a capacitively coupled output, a change in instantaneous voltage created at the transmitter causes current to accelerate up the feedline (if the impedance is less than infinite). And down the return path(s) as well. But according to Maxwell's equations, you also get changing magnetic and electric fields traveling along with the accelerating current up the feedline. You can't get one without the other given the known laws of physics. By the time the current waves reach the antenna feed point, the voltage there may or may not be different (magnitude and phase) from at the transmitter due to propagation speed, and impedance mismatches and reflections along the way.

• Hi Hotpaw thanks for the answer. Isn't an AC waveform traveling along a transmission line a single wave of movement of electrons, that wave having particular characteristics such as wavelength, and an electric potential and a flow of current at each particular point ? And the waves of voltage and current everyone talks about are just the measurements of those characteristics ? May 30 '21 at 2:49

Impedance can be defined as cause / effect or Z = E / I

False. All these equations are equally valid:

$$E = IR \tag 1$$

$$I = {E \over R} \tag 2$$

$$R = {E \over I} \tag 3$$

There is no causality inherent in this relationship. It is a three-variable relationship which can be rearranged algebraically into whatever form is most convenient.

Here's an example where the second form is convienent:

simulate this circuit – Schematic created using CircuitLab

What is the current in R1? A battery can be approximated as a voltage source. Since voltage and resistance are known, $$I = E/R$$ is useful here.

Here's an example where that's not the case:

simulate this circuit

What is the current in R1? A photodiode can be approximated as a current source. Since current and resistance are known, $$E = IR$$ is useful here.

What about this:

simulate this circuit

What resistance is required for the current through the LED to be 15 mA? Now you want $$R = E/I$$.

The causality you mention does not exist. Stop thinking about it that way. An antenna captures some (very small) power from the electromagnetic field and transfers it to the feedpoint. To transfer power, both current and voltage must be nonzero. One does not cause the other, but they are related by the feedpoint impedance.

• Sorry Phil i don't agree with you, what John Shive says in the Youtube video makes far more sense to me. youtube.com/watch?v=DovunOxlY1k Jun 2 '21 at 12:39
• @Andrew Shive is giving a specific example. You can't generalize that to all cases. He's also using an analogous device which is quite ingenious, but there are limits to the analogy. A transmission line could be considered as driven by a voltage source or a current source and we can freely pick either or convert between the two as convenient. Jun 3 '21 at 11:42