lesson
Updated 6 days ago Β· 2 views
When you plug an electric heater into a wall outlet, the alternating voltage reverses direction dozens of times every second. Does the current flow in immediate lockstep, or does it hesitate and lag behind?
In a purely resistive circuit, electric current mirrors voltage instantaneously at every microsecond with zero time delay.
Instantaneous Ohm's Law
In 1827, Georg Ohm published experimental evidence showing current is directly proportional to potential difference. In AC circuits, this relationship holds true at every single point in time: v(t)=i(t)β
R.
If an AC source supplies a sinusoidal voltage v(t)=Vpeakβsin(Οt), dividing by resistance R yields the instantaneous current expression.
i(t)=Rv(t)β=RVpeakββsin(Οt)=Ipeakβsin(Οt)
Because both waveforms share the exact same angular frequency Ο and zero initial angle offset, we say the voltage and current are in phase.
πCreate an interactive visual demonstrating in-phase AC waveforms for a purely resistive circuit. Show two synchronized sine waves over 2 full cycles (0 to 4Ο rad): Voltage v(t) in bright blue (#2563eb) with peak +10V, and Current i(t) in vibrant amber (#d97706) with peak +5A. Include vertical dotted guide lines highlighting key sync points: simultaneous positive peaks, simultaneous zero crossings, and simultaneous negative peaks. Below the graph, add a clean readout card showing 'Phase Difference Ο = 0Β° (0 rad)' and dynamic markers showing both waves crossing zero at t = 0, Ο, 2Ο, etc. Clean modern styling with dark slate text (#1e293b), light card background (#ffffff), and subtle border (#e2e8f0).
How do electrical engineers visualize this synchronized motion without drawing long sine waves across the page?
Phasor Representation
A phasor is a rotating vector that represents the magnitude and phase angle of a sinusoidal quantity in polar form.
Because current and voltage peak at the exact same instant, their phase angle difference Ο=ΞΈvββΞΈiβ equals strictly 0β (0Β rad).
πCreate a split-screen phasor and waveform interactive diagram for a purely resistive AC circuit. On the left: a polar phasor plane with reference axis 0Β°. Both the Voltage phasor V (longer blue arrow) and Current phasor I (shorter amber arrow) point along the exact same ray with angle ΞΈ = 0Β°, rotating counterclockwise together at angular velocity Ο. On the right: the corresponding generated sine waves v(t) and i(t) showing identical phase. Add clear labels: 'V and I are collinear (ΞΈ = 0Β°)' and a toggle to pause/play the rotation.