A series RLC circuit has a capacitor with a capacitance of 18.0 μF , an inductor with an inductance of 1.40 H and a resistor with a resistance of 105 Ω. The circuit has a rms current of 7.50 A when the frequency is 64.0 Hz. What is the phase angle?
Question
A series RLC circuit has a capacitor with a capacitance of 18.0 μF , an inductor with an inductance of 1.40 H and a resistor with a resistance of 105 Ω. The circuit has a rms current of 7.50 A when the frequency is 64.0 Hz. What is the phase angle?
Solution
The phase angle (ϕ) in an RLC circuit can be calculated using the formula:
ϕ = arctan((XL - XC) / R)
where:
- XL is the inductive reactance, calculated as XL = 2πfL
- XC is the capacitive reactance, calculated as XC = 1 / (2πfC)
- R is the resistance
- f is the frequency
Let's calculate XL and XC first:
XL = 2π * 64 Hz * 1.40 H = 565.49 Ω XC = 1 / (2π * 64 Hz * 18.0 μF) = 139.63 Ω
Now we can calculate the phase angle:
ϕ = arctan((565.49 Ω - 139.63 Ω) / 105 Ω) = arctan(4.05) = 76.26 degrees
So, the phase angle is approximately 76.26 degrees.
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