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A series RLC circuit has a capacitor with a capacitance of 42.0 μF , an inductor with an inductance of 0.200 H and a resistor with a resistance of 74.0 Ω. The circuit is attached to a source that has a rms voltage of 83.0 V and a frequency of 53.0 Hz. What is the phase angle?

Question

A series RLC circuit has a capacitor with a capacitance of 42.0 μF , an inductor with an inductance of 0.200 H and a resistor with a resistance of 74.0 Ω. The circuit is attached to a source that has a rms voltage of 83.0 V and a frequency of 53.0 Hz. What is the phase angle?

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Solution

The phase angle (ϕ) in a series RLC circuit can be calculated using the formula:

ϕ = arctan((XL - XC) / R)

where: XL is the inductive reactance, XC is the capacitive reactance, and R is the resistance.

First, we need to calculate XL and XC.

The inductive reactance (XL) is calculated using the formula:

XL = 2πfL

where: f is the frequency, and L is the inductance.

Substituting the given values:

XL = 2π * 53 Hz * 0.200 H = 66.8 Ω

The capacitive reactance (XC) is calculated using the formula:

XC = 1 / (2πfC)

where: C is the capacitance.

Substituting the given values:

XC = 1 / (2π * 53 Hz * 42.0 μF) = 0.057 Ω

Now, we can calculate the phase angle:

ϕ = arctan((66.8 Ω - 0.057 Ω) / 74.0 Ω)

ϕ = arctan(66.743 / 74.0)

ϕ = 41.8 degrees

So, the phase angle is 41.8 degrees.

This problem has been solved

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