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

Resonant frequency f0 = 1/(2π√(LC)) = 1/(2π√(0.2 * 10e-6)) = 159.15Hz.

Using Z = √(R² + Xl²), we have 40 = √(30² + Xl²). Solving gives Xl = 10 Ω.

Using Z = √(R² + (XL - XC)²), we find XL = √(50² - 30²) + 20 = 10Ω.

For resonance in a series RLC circuit, the condition XL = XC must be met.

When light reflects off a denser medium, a phase change of π occurs, leading to destructive interference for certain path differences.

At the center of a thin film, constructive interference occurs for longer wavelengths (red light), making red the dominant color seen.

If destructive interference occurs for blue light, the color seen will be the complementary color, which is red.

At the center of the thin film interference pattern, the color that appears is typically green due to the constructive interference of wavelengths in that range.

The color that appears at the center of the pattern corresponds to the wavelength that experiences constructive interference, which in this case is red light.

If the film thickness causes constructive interference for blue light, blue will appear at the center of the pattern.

The radius of the circular path is directly proportional to the speed of the charged particle in a uniform magnetic field.

The magnetic force is maximum when the angle between the conductor and the magnetic field is 90 degrees, as sin(90°) = 1.

In a vacuum, light travels the fastest at approximately 3 x 10^8 m/s, while sound and water waves require a medium to travel.

For a zero-order reaction, the rate is constant and does not depend on the concentration of reactants. The unit of the rate constant (k) is mol/L·s.

In a zero-order reaction, the rate is constant and does not depend on the concentration of the reactants.

The RMS value of a cosine function is I0/√2.

Inductive reactance (XL) = 2πfL = 2π(60)(0.2) ≈ 75.36Ω.

Capacitive reactance XC = 1/(2πfC) decreases as frequency f increases.

Inductive reactance (XL = 2πfL) increases with an increase in frequency.

The angle θ can be found using cos(θ) = power factor. Therefore, θ = cos⁻¹(0.8) ≈ 36.87°.

The total impedance Z = √(R² + XL²) = √(10² + 20²) = √(100 + 400) = √500 = 22.36 ohms.

The impedance Z = √(R² + XL²) = √(10² + 20²) = √(100 + 400) = √500 = 22.36 ohms.

The total impedance Z = √(R² + XL²) = √(10² + 20²) = √(100 + 400) = √500 = 22.36Ω.

Impedance Z = V/I = 100V/5A = 20Ω.

Real power P = V * I * power factor = 120 * 10 * 0.8 = 960 W.

Apparent power S = V * I = 120 V * 10 A = 1200 VA.

Power factor = Real Power / (Voltage × Current) = 600 / (120 × 10) = 0.5.

Real power P = V * I * power factor = 120V * 10A * 0.8 = 960W.

Power factor = Real Power / (Voltage x Current) = 600 / (120 x 10) = 600 / 1200 = 0.5.