A coil of inductance 15 miliherz and resistance 75 ohms in series with 8 microfaraigh capacitor is connected to a 500v / 200Hz supply calculate
1, inductive reactance
2, capacitive reactance
3, impedance
4, current
5, the phase difference between voltage and current
1. Inductive Reactance:
XL = 2πfL
XL = 2π * 200 * 15 * 10^-3
XL = 188.5 ohms
2. Capacitive Reactance:
XC = 1 / (2πfC)
XC = 1 / (2π * 200 * 8 * 10^-6)
XC = 99.88 ohms
3. Impedance:
Impedance (Z) = √(R^2 + (XL - XC)^2)
Z = √(75^2 + (188.5 - 99.88)^2)
Z = √(5625 + 7303.96)
Z = √12928.96
Z = 113.73 ohms
4. Current:
I = V / Z
I = 500 / 113.73
I = 4.39 A
5. Phase Difference:
Since the circuit contains both inductive and capacitive elements, the phase difference (θ) between voltage and current can be calculated using the formula:
θ = tan^(-1)((XL - XC) / R)
θ = tan^(-1)((188.5 - 99.88) / 75)
θ = tan^(-1)(88.62 / 75)
θ = tan^(-1)1.1816
θ ≈ 48.1 degrees
Therefore, the phase difference between voltage and current is approximately 48.1 degrees.