# Can I use V=IR in the analysis of AC circuits?

My textbooks usually just assert this relation so I don't really know when it doesn't apply.

EDIT: Reflecting on this question, I wanted to clarify that I wanted to know if Ohm's Law is valid for the analysis of time-varying current/time varying voltage/ time varying load i.e., V(t) = I(t)R(t).

• Time to learn about impedance and phasors. Commented Jan 9, 2016 at 7:44
• @Ignacio what about disputers? :p Commented Jan 9, 2016 at 8:10
• It stil applies. However, it is much more rare to encounter a pure Resistance in AC. Often there are other reactive impedances. Commented Jan 9, 2016 at 9:12
• Capacitors, inductors act different in AC than in DC in inear circuit. Commented Jan 9, 2016 at 9:34
• @Ignacio Vazquez-Abrams What does knowing about impedance and phasors have to do with knowing if V=IR applies in AC circuits? Isn't impedance just a time-varying "resistance" expressed as a ratio of time-varying Voltage divided by time-varying Current? Commented Jan 9, 2016 at 19:27

$V=IR$ is always valid in any circuit at any frequency but there are some things to watch out for and be aware of when the frequencies get really high or when there are non-linearities such as diodes to consider.

In an AC circuit V= IR like this: -

In other words I and V follow each other and have a constant ratio to each other. That constant ratio (V/I) is still R. For other types of components like capacitors the relationship between V and I is more complex: -

Now the current is "time displaced" and does not rise and fall in sync with the voltage.

Given that any resistor has a small amount of parasitic capacitance means that at high frequencies there begins a subtle change in the phase relationship between V and I. This change gets bigger and bigger at really high frequencies and, the resistor begins to look more like a capacitor.

I've purposely not mentioned inductors just to keep the answer simple.

Simple answer: Yes, Ohm's Law still applies in AC circuits.

The difference is that AC circuits involve complex sources and impedances which vary with either time or frequency, so your $V, I, \&\ R$ aren't always real numbers, but complex expressions. Nevertheless, the relationships established in Ohms Law for DC circuits will ALWAYS apply.

Yes, generally you can, but you should also take into account electromotive force produced by C and L in your circuit at each time point.

• This doesn't sound quite right. See electromotive force: 'Electromotive force, also called emf (measured in volt), is the voltage developed by any source of electrical energy such as a battery or dynamo.' Commented Jan 9, 2016 at 12:02
• Well, may be I've selected wrong term. In russian physics school we call Electromotive Force everything that can create potential difference, including capacitor charge, or magnetic field change in the inductor. Commented Jan 9, 2016 at 12:07

It is used in DC analysis mostly. For AC analysis, you will need to learn impedances too.

• For inductors, $V = L\frac{\partial I}{\partial t}$, and for capacitors, $V = \text{initial value} + \frac{1}{C}\int_t I(t) \partial t$. This turns the analysis of AC circuits from an algebra problem into a calculus problem (differential equations). Commented Jan 9, 2016 at 15:14

Of course, the Ohms's Law is still valid in AC circuits too. However, you will have to look out for components like capacitors, inductors (commonly used in AC Circuits) which have a different behavior relative to resistors. The mathematics dealing with them, is different as it climbs up into Complex Domains.