The resonant frequency f0 = 1/(2π√(LC)) = 1/(2π√(0.1 * 100e-6)) = 159 Hz.

Using f = 1/(2π√(LC)), we find f = 1/(2π√(0.1 * 100e-6)) ≈ 159 Hz.

Using Z = √(R² + (XL)²), solve for XL.

Using Z = √(R² + X²), we find X = √(Z² - R²). Here, Z = 20Ω, R = 15Ω.

Using Z = √(R² + X²), we find X = √(Z² - R²) = √(50² - 30²) = √(2500 - 900) = √1600 = 40 ohms.

The resonant frequency f of an RLC circuit is given by f = 1/(2π√(LC)).

Capacitive reactance Xc = 1 / (2πfC) = 1 / (2π * 60 * 10e-6) = 265.26Ω.

Xc = 1 / (2πfC) = 1 / (2π × 50 × 10 × 10^-6) = 318.31 ohms.

Increasing capacitance increases the current in a capacitive AC circuit, as current I = V/Xc.

Capacitive reactance Xc = 1/(2πfC), so increasing frequency decreases Xc.

The impedance of a capacitor decreases with increasing frequency.

Inductive reactance Xl = ωL increases with frequency since Xl = 2πfL.

The total impedance can increase or decrease depending on the relationship between R, XL, and XC as frequency changes.

In a parallel RLC circuit, the total current is calculated using I = V/(1/R + 1/X), where X is the total reactance.

The average power P in an AC circuit is given by P = VI cos(φ), where φ is the phase angle.

The average power consumed in an AC circuit can be expressed as P = VI, P = V²/R, and P = I²R.

The resonant frequency f of an RLC circuit is given by f = 1/(2π√(LC)).

The total impedance in a parallel circuit is given by 1/Z = 1/Z1 + 1/Z2 + 1/Z3.

Impedance Z = √(R² + X²) = √(4² + 3²) = √(16 + 9) = √25 = 5 ohms.

Impedance Z = √(R² + (XL)²), where XL = 2πfL = 31.42Ω. Thus, Z = √(10² + 31.42²) = 15.71Ω.

Impedance Z = √(R² + (XL)²), where XL = 2πfL = 31.42Ω. Thus, Z = √(10² + 31.42²) = 15.71Ω.

Impedance Z = √(R² + (1/(ωC))²) where ω = 2πf. Here, R = 4Ω, C = 2μF, f = 50Hz. Calculate Z.

At resonance, the impedance is equal to the resistance, which is 4Ω.

The impedance Z in a series RL circuit is given by Z = √(R² + (2πfL)²).

The impedance Z in a series R-L circuit is given by Z = √(R² + (ωL)²).

θ = tan⁻¹(X/R) = tan⁻¹(40/30) = 53.13°.

In a purely resistive circuit, the voltage and current are in phase, so the phase difference is 0°.

At resonance in a series RLC circuit, the phase difference between voltage and current is 0°.

Power = V × I × Power Factor = 230V × 5A × 0.8 = 920W.

Power factor = R/Z = 5/√(5² + 5²) = 5/√50 = √2/2.