A circular coil of radius 8.0 cm and 500 turns is rotated with constant angular speed 120 rad s⁻¹ about a diameter in a uniform magnetic field of magnitude 0.30 T. The coil is connected to an external resistor of resistance 10 Ω.
(i) Derive an expression for the instantaneous current in the external resistor as a function of time.
(ii) Obtain an expression for the average electrical power dissipated in the resistor over one complete cycle of rotation.
(iii) Calculate the numerical value of this average power.