--- title: "Impedance and Phasors in AC Circuits" description: "Resistors, capacitors and inductors each set a different phase between current and voltage, and rotating phasors add those voltages without trigonometric identities. Impedance packages size and phase " 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: 2026-09-12 --- > **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, and rotating phasors add those voltages without trigonometric identities. Impedance packages size and phase in one quantity. 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 that refuse to line up Each lone AC element has its own personality. A resistor lets current track voltage exactly in step. A capacitor passes current first, with voltage lagging a quarter cycle behind and size scaled by Xc equals 1 over omega C. An inductor flips it: voltage leads, current lags a quarter cycle, scaled by XL equals omega L. Frequency treats them oppositely: capacitors open up at high frequency while inductors choke. **Example.** In a series RLC circuit the three voltage arrows refuse to line up, so draw them as phasors. Put resistor voltage along the current, capacitor voltage a quarter turn behind, inductor voltage a quarter turn ahead. The vector sum is the supply voltage. Its length gives Z equals sqrt(R squared plus (XL minus Xc) squared), and its angle gives the phase lag phi, with tan phi equal to (XL minus Xc) over R. Read the diagram like a weather map. Below resonance the capacitor rules and current leads; above it the inductor rules and current lags. When XL matches Xc the two arrows wipe each other out and the circuit looks purely resistive. That cancellation is resonance: impedance bottoms at R and current peaks in step with the supply. **Tip.** Work every series AC problem in this order. Compute XL and Xc first at the given frequency. Sketch the three arrows and read Z from the total length. Read phi from the tilt, then use the AC Ohm rule, current amplitude equals voltage amplitude over Z. Never add the three voltages as plain numbers. **Recap.** Resistors stay in step, capacitors lead current by a quarter cycle, inductors lag it, and phasor arrows add the three voltages into Z and phi. ## Practice 8 questions on this page, each with its working shown. ## Needs first - [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) - [Oscillations in LC and RLC Circuits](https://lightmysky.com/learn/science/oscillations-in-lc-and-rlc-circuits-mt_QJsqX7xzkZ) - [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)