Phasor Diagram — Series LCR Circuit
I (ref) V_R V_L V_C V (net) φ V_L > V_C → Inductive (I lags V) Phasor Diagram: Series LCR (Inductive)AC Circuit Elements — Quick Comparison Table
| Parameter | Pure R | Pure L | Pure C | Series LCR at Resonance |
|---|---|---|---|---|
| Impedance | R | X_L = ωL | X_C = 1/ωC | Z = R |
| Phase φ | 0° | +90° (V leads I) | −90° (I leads V) | 0° |
| Power factor | 1 | 0 | 0 | 1 |
| Avg power | V_rms I_rms | 0 | 0 | V_r/R (max) |
| Frequency effect | None | X_L ↑ with f | X_C ↓ with f | I is maximum |
Transformer Summary Table
| Type | N ratio | V ratio | I ratio | Use |
|---|---|---|---|---|
| Step-up | N_s > N_p | V_s > V_p | I_s < I_p | Power transmission (HV) |
| Step-down | N_s < N_p | V_s < V_p | I_s > I_p | Household supply, chargers |
| Ideal | Any | V_s/V_p = N_s/N_p | I_p/I_s = N_s/N_p | P_in = P_out |
Critical Numbers for Standard Indian AC Supply
- V_rms = 220 V; = 220 × √2 ≈ 311 V; f = 50 Hz; ω = 2π×50 ≈ 314 rad/s
- Transmission voltages: 11 kV, 33 kV, 132 kV, 220 kV, 400 kV (step-up)
- Distribution: 415 V (3-phase industrial), 230 V (single-phase domestic)