Final answer:
The phase angle between the applied voltage and the current in an RLC circuit with a resistance of 560 ohms and an inductance of 10 mH at a frequency of 200Hz is 1.28 degrees. The inductive reactance is 12.56 ohms, and since the circuit is inductive, the current lags behind the voltage.
Step-by-step explanation:
Determining the Phase Angle in an RLC Circuit
To determine the phase angle between the applied voltage and the current in a circuit with a resistance (R) of 560 ohms, an inductance (L) of 10 mH, at a frequency (f) of 200Hz, we must find the inductive reactance (XL) and then use it to calculate the phase angle (φ). Since the applied voltage is specified to have a phase angle of 0 degrees, this means that the voltage is our reference phase and the current phase will be either leading or lagging based on the reactance.
Calculating Inductive Reactance
The inductive reactance can be calculated using the formula:
XL = 2πfL
For an inductance of 10 mH and frequency of 200Hz:
XL = 2π(200Hz)(10 x 10-3 H) = 12.56 ohms
Calculating the Phase Angle
The phase angle is determined using the arctangent of the ratio of the inductive reactance to the resistance:
φ = arctan(XL/R)
φ = arctan(12.56 ohms / 560 ohms) = 1.28 degrees
Therefore, the phase angle between the current and the applied voltage is 1.28 degrees, with the current lagging the voltage because the circuit is inductive in nature.