Phase angle: An LRC series circuit has voltage supplied to it at a frequency of 13.0 kHz with a phase difference between the current and the voltage of magnitude 0.20 rad. If the circuit has a capacitance of 5.0 μF and an inductance of 0.050 H find the resistance of the circuit.

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The phase angle is given by:$$\phi = \arctan\left(\frac{XL - XC}{R}\right)$$where XL is the inductive reactance, XC is the capacitive reactance, and R is the resistance.We are given that the phase angle is 0.20 rad, the capacitance is 5.0 μF, and the inductance is 0.050 H. We can use the following equations to find the inductive reactance and capacitive reactance:$$XL = 2\pi fL = 2\pi (13.0 kHz)(0.050 H) = 1.63 k\Omega$$$$XC = \frac{1}{2\pi fC} = \frac{1}{2\pi (13.0 kHz)(5.0 \mu F)} = 2.42 k\Omega$$Substituting these values into the equation for the phase angle, we get:$$0.20 rad = \arctan\left(\frac{1.63 k\Omega - 2.42 k\Omega}{R}\right)$$Solving for R, we get:$$R = 0.99 k\Omega$$Therefore, the resistance of the circuit is 0.99 kΩ.

Phase Angle: an LRC Series Circuit Has Voltage Supplied to It