Part of JMAG-03 — Alternating Current: LCR, Resonance & Transformers

Key Formulas and JEE Strategy

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Essential formulas: VrmsV_{rms} = V0sqrt\frac{V_0}{sqrt}(2). XLX_L = omegaL. XCX_C = 1omegaC\frac{1}{omega*C}. Z = sqrt(R2R^2 + (X_{L-X}_C)^2). tan(phi) = XLXCR\frac{X_L-X_C}{R}. cos(phi) = RZ\frac{R}{Z}. P = VI*cos(phi) = I2I^2*R. omega0omega_0 = 1/sqrt(LC). Q = omega0omega_0L/R = 1R\frac{1}{R}sqrtLC\frac{L}{C}. Bandwidth = RL\frac{R}{L}. Transformer: VsV_s/VpV_p = NsNp\frac{N_s}{N_p}, VpV_pIpI_p = VsV_sIsI_s.

JEE strategy: (1) Always convert to RMS before using power formulas. (2) Draw the impedance triangle — it immediately gives Z, phi, and cos(phi). (3) At resonance: Z = R, I = VR\frac{V}{R}, cos(phi) = 1 — check if the problem is at resonance first. (4) For transformer problems: first find turns ratio, then use power conservation. (5) Wattless current = I*sin(phi) — it flows but wastes no power. (6) VLV_L and VCV_C can exceed VsourceV_{source} (voltage magnification by Q). (7) In parallel LC resonance, impedance is maximum (opposite of series). (8) Choke coil = inductor used to limit current without power loss.

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