6.3 Self-assessment test 137Solution
1 From Equation (6.27) the bandwidth is given by
B - ~o0/Q(rad S -1) -- fo//Q(Hertz). Therefore
B -fo//Q = 1.02/25.64 = 0.04 MHz
2 Note that the addition of 50 f~ in the inductive branch has negligible effect
on the resonant frequency so too is unchanged. This is because, as we saw in
Example 6.9, 1/;LC ~> (R/L). /^2 Since Q - tooL~R, then with too and L
unchanged, the effect of doubling R is to halve Q and to double B. The
bandwidth is therefore doubled.6.3 SELF-ASSESSMENT TEST
1 State the condition for a series circuit containing inductance and
capacitance to be in a state of resonance.
2 Give an expression for the resonant frequency of a series RLC circuit.
3 What is the power factor of a series RLC circuit when it is in a state of
resonance?
4 A series circuit has an inductance of 2 H and a capacitance of 8 ~F. What
is its resonant angular frequency?
5 A series circuit has a resistance of 2 1), an inductance of 10 mH and a
capacitance of 0.1 I~F. What is the value of the impedance of this circuit at
resonance?
6 Explain why the voltage developed across the inductor and capacitor of a
series resonant circuit could be many times greater than the supply
voltage.
7 Define the Q-factor of a coil or circuit.
8 Give the unit of Q.
9 How may the Q-factor of a circuit be increased?
10 Explain what is meant by a 'bandpass filter'.
11 Define the bandwidth of a circuit.
12 Give the unit of bandwidth.
13 Explain the meaning of 'half-power frequency'.
14 Give the relationship between two powers P1 and P2 in decibel form.
15 State the condition for a parallel circuit containing inductance and
capacitance to be in a state of resonance.