Question
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
2, capacitive reactance
3, impedance
4, current
5, the phase difference between voltage and current
Answers
GPT 3.5
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.
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.
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