# Microwave Engineering Questions and Answers – Series and Parallel Resonant Circuits

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This set of Microwave Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Series and Parallel Resonant Circuits”.

1. In a series LCR circuit, at resonance point the energy stored in the inductor and capacitor in the form of magnetic and electric energies are equal.
a) True
b) False

Explanation: At resonant frequency of a series LCR circuit, reactance of the capacitor is equal to the reactance of the inductor. The energy stored in the capacitor in the form of electric energy and the energy stored in the inductor in the form of magnetic energy is both equal.

2. Quality factor-Q of a resonant circuit signifies:
a) Loss in the resonant circuit
b) Gain in the resonant circuit
c) Magnetic energy stored in the circuit
d) Electric energy stored in the circuit

Explanation: Quality factor of a resonant network is defined as the ratio of average energy stored to the energy loss/ second. Hence, lower loss implies a higher quality factor.

3. The total energy stored in a series RLC circuit is equal to the energy stored in the inductor.
a) True
b) False

Explanation: The total energy in an RLC circuit is the sum of the energy stored in the magnetic field of the inductor and the electric energy stored in the capacitor. Loss in the circuit occurs due to the resistive component.
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4. Higher the quality factor of a series LCR circuit, greater is the operating bandwidth of the resonant circuit.
a) True
b) False

Explanation: Band width and quality factor of a series RLC circuit are both inversely related. Higher the quality factor, lower the operating bandwidth.

5. The plot of input impedance magnitude v/s frequency has a peak at the resonant frequency.
a) True
b) False

Explanation: At resonant frequency, the capacitive reactance is equal to the inductive reactance cancelling each other’s effect. Hence, there is a dip at the center frequency in the plot of input impedance magnitude v/s frequency.

6. For a parallel resonance circuit, the plot of input impedance magnitude v/s frequency has a dip at the resonant frequency.
a) True
b) False

Explanation: In parallel RLC circuit, the input impedance is highest at resonant frequency since the reactive components are in parallel. Hence, there is a peak at the resonant frequency in the plot of input impedance magnitude v/s frequency.

7. The relation between unloaded Q and external Q is:
c) External Q = unloaded Q
d) None of the mentioned

Explanation: To compute unloaded Q only the resistance in the resonant circuit is considered. But to calculate external Q, the resistance and other load in the external load is also considered. Sine Q and R are inversely proportional, as R increases Q decreases. Since R is greater for external Q computation, unloaded Q> external Q.

8. Loaded Q and External Q are 2 different parameters.
a) True
b) False

Explanation: loaded Q and external Q are 2 different parameters. They are related by the expression
QL-1=Qe-1+ Q0-1, where QL is the loaded Q, Qe is external Q and Q0 is the unloaded Q.

9. The bandwidth of a series RLC circuit is 200 Hz. Then the quality factor of the circuit is:
a) 200
b) 100
c) 0.005
d) 0.5

Explanation: The relation between quality factor and bandwidth is given as bandwidth=Q-1. Substituting for bandwidth in this expression, the quality factor of the resonant circuit is 0.005.

10. If a parallel RLC circuit is excited with a source of 8v, 50 Hz and the circuit has an inductor of 1mH, capacitor of 1µF and a resistor of 50Ω, then the power loss that occurs in the circuit is:
a) 6.4mW
b) 3.2mW
c) 12.8mV
d) None of the mentioned

Explanation: The power loss in a parallel RLC circuit is 0.5│V│2/R. given the values of source voltage and resistance in the circuit, the power loss in the parallel RLC circuit is 6.4mW.

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