Juctor in Figur ding all insulated metal wire around a core of soft magnetic material ferrite The cylindrical coil has 9 turns a length of 458 mm and a diameter of 16 mm The core has a relative permeability of 325 and negligible resistance End Y End X iii iv End P Oll Figure Q1a A cylindrical coil inductor At t 0 s the student completes a series circuit by connecting end X of the wire to the positive terminal of a power supply and end Y to a 10 2 resistor that was connected to the negative terminal of the supply The power supply has an emf of 12 V and a negligible internal resistance i i ii iii End Q a i Show that the inductance of this inductor is approximately 15 H Calculate the time constant of this LR circuit ii Calculate the current in the circuit at time t 3 us Calculate the time taken for the current in the circuit to reach 1 1 A The student leaves the inductor connected to the power supply until the current reaches a steady value b Calculate the magnitude of the magnetic field strength inside the inductor Which end P or Q of the inductor is the North pole State the name of the rule you have used to determine this How much magnetic flux is coming out of the North pole of the inductor Calculate the amount of energy stored within the magnetic field of the inductor The student now places the inductor and the 10 resistor in series with a 180 nF capacitor and an 80 kHz AC power supply of negligible internal resistance c Calculate the capacitive reactance the inductive reactance the impedance and the phase angle for this LCR circuit and hence draw a fully labelled phasor diagram showing all of these values Finally the student removes the AC power supply and uses the series inductor and capacitor combination from part c within a radio receiver circuit d Calculate the wavelength of the radio signal that this circuit will pick up 11 5 6 3