Phasors: the spinning arrows of AC ⚡️
When you connect a resistor to an AC source, the current “keeps step” with the voltage. But the moment you add an inductor or capacitor, one of them gets ahead or lags behind. To see who leads and by how much, we draw phasors—rotating arrows that make the timing crystal-clear. :contentReference[oaicite:0]{index=0}
1 · What is a phasor? 🧭
- A phasor is an arrow that spins round and round at the circuit’s angular frequency \( \omega \).
- The arrow’s length equals the peak value (amplitude) of the quantity it represents: \( |{\vec V}| = V_m \) for voltage and \( |{\vec I}| = I_m \) for current. :contentReference[oaicite:1]{index=1}
- The vertical projection of the arrow gives the instantaneous value: \( v = V_m \sin(\omega t) \) or \( i = I_m \sin(\omega t) \). :contentReference[oaicite:2]{index=2}
- The arrow completes one full turn in the same time the AC signal finishes one cycle.
⏳ Think of the phasor like the hand of a clock that moves smoothly, while its shadow on the wall wiggles up and down like a sine wave!
2 · Drawing the phasor diagram ✏️
Place the tail of each arrow at the origin and let them rotate together. At any instant:
- The height of each arrow shows the actual voltage or current at that moment.
- The angle between two arrows tells you their phase difference.
For a pure resistor, the voltage arrow \( {\vec V} \) and the current arrow \( {\vec I} \) point in exactly the same direction. That means their phase angle is \( 0^\circ \) — they rise and fall together. :contentReference[oaicite:3]{index=3}
3 · Why phasors are handy 🛠️
- They turn tricky “sine-plus-cosine” math into simple vector addition.
- You can instantly see which quantity leads or lags.
- They are the launchpad for analyzing R-L, R-C, and R-L-C circuits (coming up in later sections!).
Note: Voltage and current themselves are scalars; the arrows are just a clever pictorial trick that follows the same math rules as true vectors. :contentReference[oaicite:4]{index=4}
Important Concepts for NEET 🎯
- Definition of a phasor – a rotating arrow of length equal to the peak value and angular speed \( \omega \).
- Projection rule – the vertical component equals the instantaneous value \( v = V_m \sin(\omega t) \) or \( i = I_m \sin(\omega t) \).
- In-phase condition – for a pure resistor, voltage and current phasors overlap; phase angle \( \phi = 0^\circ \).
- Phase tracking – the angular separation of phasors directly shows who leads or lags.
- Diagram utility – phasor diagrams simplify AC circuit analysis, making vector addition your best friend.
😊 Happy phasor-sketching, and good luck with your NEET prep!
