(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\(_c\) and the inductive reactance X\(_L\), 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: (\(\alpha\)) f = f\(_o\); (\(\beta\)) f < f\(_o\) ; (\(\gamma\))f\(_o\); when f\(_o\) 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. [\(\pi\) = 3.142].
(a)i) Explanation 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) \(\alpha\) Relationship between current and voltage when f = f\(_o\);
Current is in phase with the supply voltage (\(\beta\))
- Relationship when current and voltage when f = f\(_o\);
Current lags the Supply voltage (\(\gamma\))
- Relationship between current and voltage when f > f\(_o\);
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 = \(\omega\)BAN
480 = \(\omega\) x 0.25 x \(\pi\) x (\(\frac{8.0 \times 10^{-2}}{2}\)) x 500 = \(\omega\) = 763.8 rad/s
(c)(i) Explanation 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
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