41 public questions tagged with this topic.
**Transformer principle** alternating current in primary creates changing flux linking secondary, emf induced e = -N dΦ/dt, flux same through both, so V∝N. For N_p=550, N_s=1100, V_p=110 V rms, V_s= V_p×N_s/N_p=220 V, step-up factor 2, efficiency
Ref: NCERT > Physics Book > Alternating Currents > Transformer, AC Generator and LC Oscillations
**AC generator** converts mechanical to electrical, emf e = N B A ω sin ωt, maximum e₀ = N B A ω, frequency = rotation frequency, transformer cannot work on DC because steady flux no induction, LC oscillations energy swaps between ½ L I² and ½ Q²/C at ω₀=1/√(LC). RMS current: I = (V/R) . Given: V = 240 V , R = 120 Ω . I = (240/120) = 2 A . Applying X_L = ωL, X_C = 1/ωC, Z = √(R² + (X_L - X_C)²), I_rms = V_rms/Z, P = V_rms I_rms cosφ, V_s/V_p = N_s/N_p, calculation gives 2 A, consistent with phasor
Ref: NCERT > Physics Book > Alternating Currents > Transformer, AC Generator and LC Oscillations
**Transformer** works on mutual induction, V_s/V_p = N_s/N_p, I_s/I_p = N_p/N_s for ideal (power conserved V_p I_p = V_s I_s), step-up N_s>N_p V_s>V_p I_s
Ref: NCERT > Physics Book > Alternating Currents > Transformer, AC Generator and LC Oscillations
**Average power in LCR** P_avg = V_rms I_rms cos φ, cos φ = R/Z power factor, φ phase between V and I, tan φ = (X_L - X_C)/R. For R=80 Ω, X_L=100 Ω, X_C=40 Ω, X_L-X_C=60 Ω, Z=√(80²+60²)=100 Ω, cos φ=0.8, V_rms=240 V, I_rms=2.4 A, P=240×2.4×0.8=460.8 W, only R dissipates. X_C = (1/ω C) , ω = 2π × 60 = 376.8 rad/s . C = 23 × 10⁻⁶ F . X_C = (1/376.8 × 23 × 10⁻⁶) ≈ 115.4 Ω . RMS current: I = (V/X_C) = (110/115.4) ≈ 0.953 A . Applying X_L = ωL, X_C = 1/ωC, Z = √(R² + (X_L
Ref: NCERT > Physics Book > Alternating Currents > Power in AC Circuits - Power Factor and Wattless Current
**At resonance** V_L = I X_L = I X_C = V_C, may be larger than source voltage Q times, Q-factor = ω₀ L/R =1/(ω₀ C R)= V_L/V = V_C/V, measures sharpness, higher Q sharper resonance, bandwidth Δω = R/L = ω₀/Q, resonant frequency independent of R. X_C = (1/ω C) , ω = 2π × 60 = 376.8 rad/s . C = 17 × 10⁻⁶ F . X_C = (1/376.8 × 17 × 10⁻⁶) ≈ 156 Ω . RMS current: I = (V/X_C) = (110/156) ≈ 0.705 A . Applying X_L = ωL, X_C = 1/ωC, Z = √(R² + (X_L - X_C)²), I_rms =
Ref: NCERT > Physics Book > Alternating Currents > Resonance in LCR Circuit and Q-Factor
**Resonance in LCR** occurs when X_L = X_C, ω₀ =1/√(LC), f₀=1/(2π√(LC)), impedance Z=R minimum, current maximum I₀=V/R, circuit behaves as if only resistance because inductive and capacitive voltages equal opposite cancel, net reactance zero, phase φ=0°, power factor 1, current in phase with voltage. X_C = (1/ω C) , ω = 2π × 50 = 314 rad/s . C = 24 × 10⁻⁶ F . X_C = (1/314 × 24 × 10⁻⁶) ≈ 132.6 Ω . RMS current: I = (V/X_C) = (230/132.6) ≈ 1.734 A . Applying X_L = ωL, X_C = 1/ωC, Z = √(R² + (X_L - X_C)²), I_rms = V_rms/Z, P
Ref: NCERT > Physics Book > Alternating Currents > Resonance in LCR Circuit and Q-Factor
**Resonance in LCR** occurs when X_L = X_C, ω₀ =1/√(LC), f₀=1/(2π√(LC)), impedance Z=R minimum, current maximum I₀=V/R, circuit behaves as if only resistance because inductive and capacitive voltages equal opposite cancel, net reactance zero, phase φ=0°, power factor 1, current in phase with voltage. X_C = (1/ω C) , ω = 2π × 50 = 314 rad/s . C = 26 × 10⁻⁶ F . X_C = (1/314 × 26 × 10⁻⁶) ≈ 122.4 Ω . RMS current: I = (V/X_C) = (230/122.4) ≈ 1.879 A . Applying X_L = ωL, X_C = 1/ωC, Z = √(R² + (X_L - X_C)²), I_rms = V_rms/Z, P
Ref: NCERT > Physics Book > Alternating Currents > Resonance in LCR Circuit and Q-Factor
**At resonance** V_L = I X_L = I X_C = V_C, may be larger than source voltage Q times, Q-factor = ω₀ L/R =1/(ω₀ C R)= V_L/V = V_C/V, measures sharpness, higher Q sharper resonance, bandwidth Δω = R/L = ω₀/Q, resonant frequency independent of R. At resonance, Z = R = 50 Ω . RMS current: I = (V/R) = (250/50) = 5 A . Applying X_L = ωL, X_C = 1/ωC, Z = √(R² + (X_L - X_C)²), I_rms = V_rms/Z, P = V_rms I_rms cosφ, V_s/V_p = N_s/N_p, calculation gives 5 A, consistent with phasor analysis and resonance condition X_L = X_C.
Ref: NCERT > Physics Book > Alternating Currents > Resonance in LCR Circuit and Q-Factor
**Resistor in AC** behaves as DC, no reactance, impedance Z=R, current follows voltage exactly, average power over cycle V_rms I_rms, for 200 V rms, 80 Ω, P=500 W? Actually 200²/80=500 W, peak current √2×2.5=3.535 A, average power ½ V_peak I_peak. RMS current: I = (V/R) . Given: V = 75 V , R = 15 Ω . I = (75/15) = 5 A . Applying X_L = ωL, X_C = 1/ωC, Z = √(R² + (X_L - X_C)²), I_rms = V_rms/Z, P = V_rms I_rms cosφ, V_s/V_p = N_s/N_p, calculation gives 5 A, consistent with phasor analysis and resonance condition X_L = X_C.
Ref: NCERT > Physics Book > Alternating Currents > AC Through Resistor - Phasor and Power
**At resonance** V_L = I X_L = I X_C = V_C, may be larger than source voltage Q times, Q-factor = ω₀ L/R =1/(ω₀ C R)= V_L/V = V_C/V, measures sharpness, higher Q sharper resonance, bandwidth Δω = R/L = ω₀/Q, resonant frequency independent of R. At resonance, Z = R = 40 Ω . RMS current: I = (V/R) = (200/40) = 5 A . Applying X_L = ωL, X_C = 1/ωC, Z = √(R² + (X_L - X_C)²), I_rms = V_rms/Z, P = V_rms I_rms cosφ, V_s/V_p = N_s/N_p, calculation gives 5 A, consistent with phasor analysis and resonance condition X_L = X_C.
Ref: NCERT > Physics Book > Alternating Currents > Resonance in LCR Circuit and Q-Factor
**Capacitor average power** zero over complete cycle because P=V I =½ V_peak I_peak sin2ωt average zero, energy stored in field, not dissipated, unlike resistor. For 15 μF, 60 Hz, X_C=176.8 Ω, V_rms=110 V, I_rms=0.622 A, illustrating lower C higher X_C. X_C = (1/ω C) , ω = 2π × 50 = 314 rad/s . C = 28 × 10⁻⁶ F . X_C = (1/314 × 28 × 10⁻⁶) ≈ 113.6 Ω . RMS current: I = (V/X_C) = (220/113.6) ≈ 1.936 A . Applying X_L = ωL, X_C = 1/ωC, Z = √(R² + (X_L - X_C)²), I_rms = V_rms/Z, P = V_rms I_rms cosφ,
Ref: NCERT > Physics Book > Alternating Currents > AC Through Capacitor - Capacitive Reactance
**Capacitor average power** zero over complete cycle because P=V I =½ V_peak I_peak sin2ωt average zero, energy stored in field, not dissipated, unlike resistor. For 15 μF, 60 Hz, X_C=176.8 Ω, V_rms=110 V, I_rms=0.622 A, illustrating lower C higher X_C. X_L = ω L , ω = 2π × 50 = 314 rad/s . L = 30 × 10⁻³ H . X_L = 314 × 0.03 = 9.42 Ω . RMS current: I = (V/X_L) = (220/9.42) ≈ 23.35 A . Applying X_L = ωL, X_C = 1/ωC, Z = √(R² + (X_L - X_C)²), I_rms = V_rms/Z, P = V_rms I_rms cosφ, V_s/V_p =
Ref: NCERT > Physics Book > Alternating Currents > AC Through Capacitor - Capacitive Reactance
