Q1. An LC circuit has L = 2 H and C = 8 µF. Find its resonant frequency.
f = 1 / (2π√(LC))
√(LC) = √(2 × 8×10⁻⁶) = √(1.6×10⁻⁵) = 4×10⁻³
f = 1 / (2π × 4×10⁻³) ≈ 39.8 Hz
Alternating Current — Class 12
The electricity in your home is alternating. Learn RMS values, reactance and resonance, and use the transformer calculator that steps voltage up and down.
AC & RMS valueAlternating current reverses direction periodically. The RMS (effective) value delivers the same power as a DC of that value: I_rms = I₀/√2.
ReactanceThe opposition of an inductor (X_L = ωL) or capacitor (X_C = 1/ωC) to AC. Unlike resistance, it depends on frequency.
Impedance & resonanceTotal opposition Z = √(R² + (X_L − X_C)²). At resonance X_L = X_C, Z is minimum and current is maximum.
TransformerChanges AC voltage using two coils: V_s/V_p = N_s/N_p. Step-up increases voltage; step-down decreases it (power is conserved).
RMS & transformer calculator Interactive
Convert peak voltage to RMS, and find a transformer's output voltage from its turns ratio.
RMS voltage, V₀/√2—V
Output voltage, V_p·N_s/N_p—V
India's "220 V" mains is the RMS value; the peak is about 311 V. A transformer only works with AC, not DC.
Numericals practice Interactive
RMS and transformer problems with steps.
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Solved numericals
Q2. A step-down transformer converts 2200 V to 220 V. If the primary has 5000 turns, find the secondary turns.
N_s/N_p = V_s/V_p = 220/2200 = 1/10
N_s = 5000 / 10 = 500 turns
Formula sheet
| Quantity | Formula | SI unit |
|---|---|---|
| RMS voltage | V_rms = V₀ / √2 | volt (V) |
| Inductive reactance | X_L = 2πf L | ohm (Ω) |
| Capacitive reactance | X_C = 1 / (2πf C) | ohm (Ω) |
| Resonant frequency | f = 1 / (2π√(LC)) | hertz (Hz) |
| Transformer | V_s / V_p = N_s / N_p | — |
Common mistakes & exam wins
- The "220 V" of household supply is the RMS voltage; the peak value is V₀ = √2 × 220 ≈ 311 V.
- Reactance depends on frequency; resistance does not. At resonance X_L = X_C.
- A transformer works only on AC because it needs a CHANGING flux; it cannot step up DC.
- In a step-up transformer voltage increases but current decreases (power V×I stays the same).
Frequently asked questions
What is the RMS value of an alternating current?
The steady DC value that would produce the same heating; I_rms = I₀/√2 and V_rms = V₀/√2.
What is resonance in an AC circuit?
The condition when X_L = X_C, so impedance is minimum and the current is maximum, at f = 1/(2π√(LC)).
How does a transformer work?
A changing current in the primary coil produces a changing flux that induces a voltage in the secondary; V_s/V_p = N_s/N_p.
Why can a transformer not work with DC?
Because DC gives a steady (unchanging) flux, and induction requires a changing flux to induce a voltage in the secondary coil.