Exercise - Series Resonance

Exercise - Series Resonance

1. A series resonant circuit has BW = 2000 Hz and Q = 100. It uses a capacitor of 50 pF. Calculate the other constants of the circuit. If an AC voltage of 1 volt is connected to this circuit, what will be the voltage across inductor, capacitor and resistor at resonance?

[Ans: R = 159.4 Ω, L = 12.67 mH, 100 volts, 100 volts & 1 volt]

2. A series RLC circuit consists of R = 1000 Ω, L = 100 milli henries and C = 10 × 10^-12 farads.

The applied voltage across the circuit is 100 V.

(i) Find the resonant frequency of the circuit.

(ii) Find the Q factor of the circuit at resonant frequency.

(iii) At what angular velocities do the half-power points occur?

(iv) Compute the band width of the circuit.

 [Ans: 0.159 × 10 Hz; 100; 995 × 10³, 1005 ×103 rad/sec; 10×10³ rad/sec]

3. A series RLC circuit has a resistance of 20 Ω, inductance of 0.05 henrys and capacitance of 10 μF. Find resonant frequency, band width and Q of the circuit.

 [Ans: ω₀ = 1414 rad/sec; BW = 400 rad/sec; Q = 3.54]

4. A series RLC circuit has the following parameter values R = 10 ohms, L = 1 H and C = 1 μF.

(a) Compute the resonant frequency in radians/sec.

(b) Calculate the quality factor of the circuit.

(c) What is the value of the bandwidth ?

(d) Calculate the lower and upper frequency points of the bandwidth in radians/sec.

[Ans: (a) 1000rad/sec; 100; 10rad/sec; 995 rad/sec; 1005 rad/sec]

5. A series RLC circuit is applied with a sinusoidal source of constant voltage and a variable frequency. If f₁ and f₂ are two frequencies at which the current in the circuit has the same magnitude, show that (i) The power factor of the circuit has the same values at f₁ and f₂ and (ii) 4π2 f₁ f₂ LC = 1.