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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?

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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.

This problem has been solved

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