WAEC Physics 2020 Theory — Question 9

Model answer

(a)(i) Resonance frequency as applied to RLC series circuit: It is the frequency of oscillation of an RLC series circuit when the capacitive reactance Xc is equal to the inductive reactance XL and the impedance Z is equal to the resistance with the current maximum and the impedance minimum. (ii) [Sketch: graph of reactance (y-axis) against frequency (x-axis), showing XL as an increasing line and Xc as a decreasing curve, intersecting at the resonance frequency fo.] (iii) Relationship between current and voltage: (alpha) When f=fo, current is in phase with the supply voltage. (beta) When f less than fo, current leads the supply voltage. (gamma) When f greater than fo, current lags the supply voltage. (b)(i) Mutual inductance is defined as the ratio of the induced e.m.f. in one coil or circuit to the time rate of change of current in the other coil. It is also defined as the production of e.m.f. in a circuit as a result of the change in the magnetic flux in an adjacent circuit linked to it. (ii) Given: Number of turns N=500 turns, diameter d=8.0cm=8x10^-2m, B=0.25T, V=480V, pi=3.142. Correlating equation: Rotational induced e.m.f of an electric generator, E.m.f.=(omega)BAN. 480=omega x 0.25 x (pi d^2/4) x 500. 480=omega x 0.25 x [(8x10^-2)^2 x pi/4] x 500. 480=6284x10^-4 (omega). omega=480/0.6284=763.84 rad/s. (c)(i) Eddy current: These are currents induced and flows within a metal block when there is a change in magnetic flux linking the block. OR They are loops of electrical current induced within conductors by changing magnetic field in the conductor. Eddy currents flow in closed loops within conductors, in planes perpendicular to the magnetic field. (ii) Practical uses of Eddy currents: Induction heating furnaces to heat objects; Automobile speedometers; Induction alternating current (AC) motors; Induction coils.