What is the phase angle between the voltage across and the current through a series RLC circuit if XC is 500 ohms, R is 1 kilohm, and XL is 250 ohms?

To find the phase angle in a series RLC circuit, first calculate the net reactance (X). Net reactance is the inductive reactance minus the capacitive reactance (X = XL - XC). In this case, 250 ohms - 500 ohms equals a net reactance of -250 ohms. Next, calculate the phase angle using the arctangent function: phase angle = arctan(X / R). Plugging in our values gives arctan(-250 / 1000) = arctan(-0.25), which is approximately -14.0 degrees. The negative sign mathematically indicates the phase relationship. Finally, determine whether the voltage leads or lags. Because capacitive reactance (XC) is greater than inductive reactance (XL), the circuit is capacitive. Using the mnemonic 'ELI the ICE man', 'ICE' tells us that Current (I) leads Voltage (E) in a Capacitor (C). If current leads voltage, then voltage lags current, making '14.0 degrees with the voltage lagging the current' the correct answer.