A homeowner has a series RLC circuit in her home's electrical system. The circuit includes an 80 Ω resistor, a 0.15 H inductor found in a ceiling fan, and a 45 μF capacitor incorporated into the lighting system. The home's electrical supply provides 240 V at a frequency of 50 Hz. Determine the phase angle ϕ.

A series RLC circuit is employed in home heating systems. It consists of an 80.0 Ω resistor, a 0.15 H inductor in the heating unit, and a 45.0 μF capacitor integrated into the thermostat. The system operates on a 240 V, 50.0 Hz power supply. Determine the average power dissipation in this circuit.

An AM radio receiver, designed to detect oscillating signals, is based on an RLC circuit with an inductance of 320 nH. This receiver is tuned to detect signals at 780 kHz. However, a nearby generator is producing signals at 750 kHz. These two generators have a frequency separation of 30 kHz, which is the minimum permissible separation for adjacent AM signal generators. To effectively combat the undesired 750 kHz signal, the peak current at this frequency should be 0.08% of the peak current at 780 kHz. Determine the maximum resistance of the RLC circuit when decoding the 780 kHz signal, assuming both generators radiate equal power.

An electric water pump powered by a motor is connected to a 220V/50Hz power outlet to analyze its torque output. The pump expends electrical energy at a rate of 1200 W when the current flowing in the motor is 15 A. Find the motor's resistance assuming the motor is in a series RLC circuit.