--- title: "Impedance and Phasors in AC Circuits" description: "Resistors, capacitors and inductors each set a different phase between current and voltage. Phasors add their voltages as vectors. Impedance magnitude Z describes the voltage-to-current amplitude rati" canonical: https://lightmysky.com/learn/science/impedance-and-phasors-in-ac-circuits-mt_vQVlVWv2ln source: https://lightmysky.com/learn/science/impedance-and-phasors-in-ac-circuits-mt_vQVlVWv2ln.md retrieved: 2026-11-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Impedance and Phasors in AC Circuits Resistors, capacitors and inductors each set a different phase between current and voltage. Phasors add their voltages as vectors. Impedance magnitude Z describes the voltage-to-current amplitude ratio, while phase angle phi describes their phase difference. Subject: Science · Area: Electricity & Magnetism · Ages 20 to 21 Page: https://lightmysky.com/learn/science/impedance-and-phasors-in-ac-circuits-mt_vQVlVWv2ln ## Ready when they can - States the reactance of a capacitor and an inductor and how each shifts the phase - Adds voltages with a phasor diagram to get the impedance of a series RLC circuit - Reads the phase angle between supply voltage and current off the diagram ## Lesson: Phasors: adding AC voltages with different phases Use sinusoidal AC in steady state with ideal components. Angular frequency is omega = 2 pi f. A resistor's voltage and current are in phase. In a capacitor, current leads voltage by a quarter cycle; Xc = 1/(omega C). In an inductor, current lags voltage by a quarter cycle; XL = omega L. Reactance is the ratio of voltage amplitude to current amplitude, measured in ohms. It is not energy loss. *(drawing: For fixed L and C, increasing frequency raises XL and lowers Xc.)* A phasor is an arrow whose length represents a sinusoid's amplitude and whose direction represents phase. In series, all elements share the same current. Take its direction as rightward: resistor voltage points right, inductor voltage up, and capacitor voltage down. The opposite vertical arrows subtract. Their sum with the resistor arrow gives supply voltage. The impedance magnitude is Z = sqrt(R^2 + (XL - Xc)^2), in ohms. For an ideal series RLC circuit with R > 0, below resonance Xc exceeds XL and current leads supply voltage. Above resonance XL exceeds Xc and current lags. At resonance XL = Xc: the reactive voltage phasors cancel and Z = R. Supply voltage and current are then in phase. For a fixed supply voltage amplitude, this minimum impedance gives the greatest current amplitude. **Example.** The current amplitude is I0 = V0/Z, where V0 is the supply voltage amplitude. Do not mix peak and rms values. For V0 = 12 V and Z = 6 ohm, I0 = 12/6 = 2 A. First find the reactances, then Z, then divide the voltage amplitude by Z. **Example.** Instantaneous signed voltages add by the loop rule. Their positive peak amplitudes usually do not, because their peaks occur at different times. Inductor and capacitor voltages are half a cycle apart. For amplitudes VR = 6 V, VL = 10 V and VC = 2 V, the net reactive amplitude is 8 V. The supply amplitude is sqrt(6^2 + 8^2) = 10 V, not 18 V. Define phi as supply voltage phase minus current phase. For R > 0, phi = arctan((XL - Xc)/R), between -90 and 90 degrees. Positive phi means current lags; negative phi means current leads. If XL - Xc equals R, tan phi = 1 and phi = 45 degrees. If XL = Xc, phi = 0. Z in this lesson is impedance magnitude; phi supplies its phase information. **Recap.** Capacitor current leads voltage; inductor current lags. Phasor addition gives Z, I0 = V0/Z and the signed phase phi. *Original lesson, questions and study cards authored by Marble.* ## Practice 8 questions on this page, each with its working shown. ## Needs first - [Oscillations in LC and RLC Circuits](https://lightmysky.com/learn/science/oscillations-in-lc-and-rlc-circuits-mt_QJsqX7xzkZ) ## Optional connections - [Combining a sine and a cosine into a single wave](https://lightmysky.com/learn/mathematics/combining-a-sine-and-a-cosine-into-a-single-wave-mt_IwQkNDRWyq) - [Euler's Formula and the Exponential Form](https://lightmysky.com/learn/mathematics/eulers-formula-and-the-exponential-form-mt_RX2IxsnSwG) ## Opens up - [Resonance and Power in AC Circuits](https://lightmysky.com/learn/science/resonance-and-power-in-ac-circuits-mt_wviaR0dJud)