.jpeg)
CLASS 12 • PHYSICS
Alternating Current
1. AC Basics
Instantaneous Current
$I = I_0 \sin(\omega t)$
RMS Value (Effective)
$I_{rms} = \frac{I_0}{\sqrt{2}} = 0.707 I_0$
Meters measure RMS, not Peak!
Average Value (Full Cycle)
$I_{avg} = 0$
Average Value (Half Cycle)
$I_{avg} = \frac{2I_0}{\pi} = 0.637 I_0$
2. Pure L, C, R Circuits
Inductive Reactance ($X_L$)
$X_L = \omega L = 2\pi f L$
Current LAGS Voltage by 90°
Capacitive Reactance ($X_C$)
$X_C = \frac{1}{\omega C} = \frac{1}{2\pi f C}$
Current LEADS Voltage by 90°
DC Blocking
For DC, $f=0 \Rightarrow X_C = \infty$ (Open Circuit)
3. Series LCR Circuit
Impedance (Z)
$Z = \sqrt{R^2 + (X_L - X_C)^2}$
Peak Current
$I_0 = \frac{V_0}{Z}$
Phase Angle ($\phi$)
$\tan\phi = \frac{X_L - X_C}{R}$
Power Factor
$\cos\phi = \frac{R}{Z}$
Pure R: $\cos\phi=1$. Pure L/C: $\cos\phi=0$
4. Electrical Resonance
Condition
$X_L = X_C \Rightarrow Z_{min} = R$
Resonant Frequency
$\omega_0 = \frac{1}{\sqrt{LC}}$
$f_0 = \frac{1}{2\pi\sqrt{LC}}$
Current at Resonance
$I_{max} = \frac{V}{R}$
Quality Factor (Q)
$Q = \frac{1}{R}\sqrt{\frac{L}{C}}$
Higher Q = Sharper Resonance
5. Power in AC
Average Power
$P = V_{rms} I_{rms} \cos\phi$
Also $P = \frac{1}{2} V_0 I_0 \cos\phi$
Wattless Current
$I_{wattless} = I_{rms} \sin\phi$
Power consumed is Zero
LC Oscillations
$\omega = \frac{1}{\sqrt{LC}}$
Energy swaps between Capacitor & Inductor
6. The Transformer
Transformation Ratio
$\frac{V_s}{V_p} = \frac{N_s}{N_p} = \frac{I_p}{I_s} = k$
Efficiency ($\eta$)
$\eta = \frac{P_{out}}{P_{in}} = \frac{V_s I_s}{V_p I_p}$
Step-Up vs Step-Down
Step-Up: $N_s > N_p$ ($V \uparrow, I \downarrow$)
Step-Down: $N_s < N_p$ ($V \downarrow, I \uparrow$)
7. Common Exam Traps
- ⚠️ Peak vs RMS: If question says "220V AC", it implies RMS value, not Peak. Peak = $220 \times \sqrt{2} \approx 311V$.
- ⚠️ Frequency Doubling: Inductive reactance $X_L$ doubles if frequency doubles. Capacitive $X_C$ halves.
- ⚠️ Transformer DC: Transformers DO NOT work on DC. Output voltage will be Zero (Flux constant).
8. Golden Theory Rules
- Choke Coil: Used to control current in AC circuits without power loss. High Inductance (L), Negligible Resistance (R).
- Capacitor Filter: Capacitor blocks DC component and passes AC component. Used in Rectifiers.
- Power Loss: In a Transformer, ideal power loss is zero. Real losses: Eddy currents, Hysteresis, Flux leakage, Copper loss ($I^2R$).
