Final answer:
The question involves calculating impedance and current in an RLC circuit, using reactances at specific frequencies to find impedance and applying Ohm's law to determine Irms.
Step-by-step explanation:
The student's question involves a series RLC circuit where the current lags the EMF by 60 degrees. The circuit's behavior changes based on the impedance at varying frequencies and component values. To calculate the circuit's impedance, we use the formula Z = √(R² + (XL - XC)²). The impedance can vary when the circuit is subject to different frequencies, as seen at 60.0 Hz and 10.0 kHz. For each frequency, we find the impedance and subsequently use Ohm's law, V = IZ, to calculate the root mean square (Irms) current when a voltage is applied.
For instance, if an RLC circuit consists of a 40.0 ohms resistor, a 3.00 mH inductor, and a 5.00 µF capacitor, we would find the impedance at a given frequency using the stated reactances from Example 23.10 and Example 23.11. Once we have the impedance, we find Irms using the given Vrms value.