# Does AC phase shift violate Ohms law?

Ok, so I am not new to electronics by any means, but I still can't grasp one key concept: AC voltage-current phase shift. I understand the math behind it, but I need someone to explain to me how it works at the fundamental level.

Let's take into consideration the circuit below. The input sine voltage is 100V and we know that inductor causes voltage to lag 90 degree behind the current.

1. My first question is does the phase shift happen in the whole circuit, or only after/before the inductor?

2. My second question is if we would measure the voltage and current flowing through the resistor R1, and since they are not in phase, doesn't this violate the Ohms law (how can maximum current flow through the resistor when it doesn't experience maximum voltage)?

Thank you.

simulate this circuit – Schematic created using CircuitLab

• The same current flows through all components in a series circuit. The voltage across the inductor leads this current by 90 degrees, the voltage across the resistor is in-phase with this current.
– Chu
Nov 29, 2019 at 0:55

The input sine voltage is 100V and we know that inductor causes voltage to lag 90 deg behind the current.

My first question is does the phase shift happen in the whole circuit, or only after/before the inductor?

The current through the entire circuit lags the supply voltage. The voltage across the inductor leads the current.

My second qustion is if we would measure the the voltage and current flowing through the resistor R1, and since they are not in phase, doesn't this violate the ohms law ...

The voltage across the resistor is in phase with the current. The amount by which the current lags the supply voltage is determined by the combined effect of the resistor and the inductor.

In every circuit, also in this circuit, the current as a function of time takes such shape that every part obeys its operating law and circuit wide Kirchoff's laws are also fulfilled. No other current form is possible.

The resistor obeys Ohm's law I=U/R where U is the voltage between the ends of the resistor.

U=generator's voltage minus inductor's voltage. That's true in every moment, the law is known as Kirchoff's voltage law.

You cannot assume arbitary voltage over the inductor. Inductor generates voltage = L * the changing rate (amperes per second) of the current. Otherwise it wouldn't be an inductor. You must find which time dependency of the current fulfills every said law. That's how the circuit works.

You didn't try to find which current vs. time fits this circuit, but made instead some fuzzy assumptions and decided "the circuit seems to violate circuit laws". As well I could say "the current=zero, so this circuit doesn't obey the laws, some of the laws are not valid just in this circuit". But serious members would vote me out quite soon.

Elementary differential equation theory tells that the only possible current in the drawn circuit is a 50Hz sinusoidal which has some phase lag behind the voltage of the generator. The lag in your numerical case is quite small, it's only 180 microdegrees, which probably means nothing practically substantial in 50Hz electric power systems.

Practical electricians like me mostly do not calculate with differential equations. Mathematicians have developed for us a shorter but still exact calculation method named phasor calculus. It can be used only with sinusoidal currents and voltages which have the same frequency.

BTW. Your question "does the phase shift happen in the whole circuit, or only after/before the inductor?" reveals there's much fog in how you understand such things as voltage, current and being connected in series. Make those things clear at first.