#high frequency

Resonance in LCR Circuit and Q-Factor

In an LCR series circuit, what happens to the circuit’s behavior when the frequency is significantly above the resonant

**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. Above resonance, X_L = ω L becomes much larger than X_C = (1/ω C) , making the net reactance positive. The circuit behaves as predominantly inductive, with the current lagging the voltage. 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

Ref: NCERT > Physics Book > Alternating Currents > Resonance in LCR Circuit and Q-Factor

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AC Through Resistor - Phasor and Power

In an AC circuit with a series combination of resistor and capacitor, what happens to the phase difference if the freque

**Current relative to voltage** in resistor in phase, φ=0°, power factor cos φ=1, maximum power, unlike inductor/capacitor where average power zero due to 90° phase shift, explaining why resistor heats while pure L/C does not. In an RC series circuit, Φ = tan⁻¹ ( (X_C/R) ) , where X_C = (1/ω C) . As frequency ( ω ) approaches infinity, X_C approaches zero, making Φ approach 0°, so the circuit becomes nearly resistive. 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 It approaches 0°, consistent with

Ref: NCERT > Physics Book > Alternating Currents > AC Through Resistor - Phasor and Power

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LCR Series Circuit - Impedance and Phasor Diagram

What is the behavior of the impedance in a series LCR circuit at very high frequencies?

**Impedance behavior at high frequencies** X_L=ωL dominates ∝ f, X_C=1/ωC →0, so Z≈√(R²+X_L²)≈X_L large, current small, circuit inductive, φ→90°, at low frequencies X_C large, Z≈X_C, capacitive, φ→-90°, at intermediate resonance Z minimal =R. At very high frequencies, X_L = ω L becomes very large, while X_C = (1/ω C) becomes very small. The impedance Z = √(R² + (X_L - X_C)²) is dominated by X_L , making the circuit behave as predominantly inductive. 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 It behaves as

Ref: NCERT > Physics Book > Alternating Currents > LCR Series Circuit - Impedance and Phasor Diagram

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Infrared, Visible Light and Applications

Why can't visible light electromagnetic waves be produced by an oscillating circuit at \( 6 \times 10^{14} \, \text{Hz}

**Visible light** λ≈400-700 nm, f≈4×10¹⁴ to 7×10¹⁴ Hz, narrow part of spectrum sensitive to human eye, produced by atomic transitions, used for vision, photosynthesis, optical fibers, central frequency ≈5×10¹⁴ Hz, different colors correspond to different λ. The document explains that modern circuits can only achieve frequencies up to 10¹¹ Hz , far below the 6 × 10¹⁴ Hz required for visible light. Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields Because achievable frequencies are much lower, illustrating EM wave transverse nature and Maxwell's di

Ref: NCERT > Physics Book > Electromagnetic Waves > Infrared, Visible Light and Applications

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