# Impedance in sine DC

If we have a DC sine signal. Can we say that capacitors and inductors have impedance despite not being AC?

If yes then what will the formula look like?

And the opposite if we have an AC square signal do capacitors and inductors have impedance?

• Can you elaborate on what you mean by DC sine signal ? If possible a mathematical expression representing such a signal. – AJN Jul 5 at 8:29
• For an AC suqare signal, the signal can be represented as the sum several sinusoids at different frequencies and amplitudes (en.wikipedia.org/wiki/Fourier_series) and analysis can be done separately for each sinusoid term (subject to some contstraints). – AJN Jul 5 at 8:31
• Sine DC is a signal produced by a full wave bridge rectifier without filters. – Maddy Wells Jul 5 at 9:04
• pulsed DC is what I mean That's DC + a pulsed shape signal, the pulse shaped signal has a value that varies over time and that means it is AC. DC does not vary over time. If it does, it is considered AC. – Bimpelrekkie Jul 5 at 10:19
• @Maddy, there are two ways of looking at it: (1) If we look at the overall current waveform and it varies but never changes direction then it's DC because the current is not alternating direction (and passing through zero). (2) If we consider the waveform as the sum of a DC and AC waveform we can, by definition, consider that it has an AC componenent. – Transistor Jul 5 at 11:46

## 2 Answers

If we have a DC sine signal. Can we say that capacitors and inductors have impedance despite not being AC?

When we talk about the impedance of an inductor or capacitor we are talking about one single frequency (a sine-wave) with no DC offset: -

$$|X_L| = 2\pi F L$$

And

$$|X_C| = \dfrac{1}{2\pi F C}$$

Where $$\F\$$ is a single operating frequency in hertz.

$$\color{red}{\boxed{\text{There's no room to consider DC or multiple frequencies}}}$$

And the opposite if we have an AC square signal do capacitors and inductors have impedance?

If we want to consider how the current might flow for an arbitrary voltage signal then we revert to the basic relationships: -

$$V = L\dfrac{di}{dt}$$

And

$$I = C\dfrac{dv}{dt}$$

For the inductor with a "square signal", when the voltage is +V, the current rises ($$\\frac{di}{dt}\$$) at a rate of $$\\frac{v}{L}\$$ amps per second and, when the "square signal" is -V, the current falls at a rate of $$\\frac{v}{L}\$$.

If we did the same for a capacitor, the rate of change of voltage ($$\\frac{dv}{dt}\$$) is infinite when the "square signal" switches so we get a pulse of infinite current. But we could assume that the "input" is current and that the current forms a square wave - now we'd get a very similar result for the inductor driven with a square voltage.

• "When we talk about the impedance of an inductor or capacitor we are talking about one single frequency (a sine-wave) with no DC offset:" This got me thinking, Andy. What difference does a DC offset make to the impedance of a capacitor? None, I think.The inductor case is conceptually a little more difficult as DC current will flow through it but the impedance at the AC frequency will be the same provided we haven't saturated the core of the inductor. Am I missing something in your thinking? – Transistor Jul 5 at 11:52
• there is no "basic relationship" like V = L*dI/dt. Do you mean EMF = -L*dI/dt here? – V.V.T Jul 5 at 12:28
• @Transistor no you're not missing anything - impedance is exclusively to do with sinewaves. – Andy aka Jul 5 at 12:30
• @V.V.T - what is the formula for current flow in an inductor when a fixed voltage is applied - it is this: $$V = L\dfrac{di}{dt}$$ – Andy aka Jul 5 at 12:31
• Current change in inductor produces EMF, not a voltage drop. Internal resistance does produces voltage drop across a non-ideal inductor, but it is altogether other story – V.V.T Jul 5 at 12:35

Capacitors and inductors always have impedance, at all frequencies, including 0 which is DC.

There is no DC sine. At DC, frequency is 0, so capacitor has impedance of infinity so it is an open circuit and inductance has impedance of zero so it is a short circuit. AC signal has a frequency, and ideal square wave consists of harmonic frequencies up to infinity, so yes, capacitors and inductors have impedance at all frequencies.

Recitified AC is also AC, even if it has an average DC component.