(a)Explain resonance frequency as applied in RLC series Circuit. (ii) Sketch a diagram to illustrate the variation of frequency, f, with the resistance, R, the capacitive reactance, X and the inductive reactance X, in RLC series circuit. (iii) Using the diagram drawn in (a)(ii) state whether the current in the circuit leads, lags or is in phase with the supply voltage when: () f = f; () f < f ; ()f; when f is the resonant frequency. b)(i) Define mutual inductance. (i) The coil of an electric generator has 500 turns and 8.0cm diameter. If it rotates in a magnetic field of density 0.25T, calculate the angular speed when its peak voltage is 480V. [ = 3.142].
Explanation
(a)i) of resonance frequency as applied to RLC series circuit - It is the frequency of oscillation of an RLC series circuit when the capacitive reactance is equal to the inductive reactance. The impedance is equal to the resistance /the impedance is minimum. (ii) A sketched graph
(iii) Relationship between current and voltage when f = f; Current is in phase with the supply voltage () - Relationship when current and voltage when f = f; Current lags the Supply voltage () - Relationship between current and voltage when f > f; Current leads the supply voltage.
(b) (i) Definition of mutual inductance: The ratio of the induced emf in one coil/circuit to the time rate of change of current in the other coil. OR The production of e.m.f in a circuit as a result of the change in the magnetic flux/magnetic circuit in an adjacent circuit linked to it . (ii) Calculation of angular speed of the coil of an electric generator: E = BAN 480 = x 0.25 x x () x 500 = = 763.8 rad/s
(c)(i) of eddy current: The current is induced and flows within a metal block when there is a change in magnetic flux linking the block. OR Loops of electric current induced within a conductor by the changing magnetic flux/field in the conductor.
OR The localised electric current/loops of electric current (ii) Practical Uses of eddy current: - induction furnaces - induction coils - speedometers - induction meters