# Network Theory Questions and Answers – Bandwidth of an RLC Circuit

This set of Network Theory Multiple Choice Questions & Answers (MCQs) focuses on “Bandwidth of an RLC Circuit”.

1. The expression of power (P1) at lower half power frequency is?
a) (I2maxR)/8
b) (I2maxR)/4
c) (I2maxR)/2
d) I2maxR

Explanation: The upper and lower cut-off frequencies are sometimes called the half-power frequencies,. At these frequencies the power from the source is half of the power delivered at the resonant frequency. The expression of power (P1) at lower half power frequency is P1 = (I2maxR)/2.

2. At upper half power frequency, the expression for power (P2) is?
a) I2maxR
b) (I2maxR)/2
c) (I2maxR)/4
d) (I2maxR)/8

Explanation: At upper half power frequency, the expression for power (P2) is P2 = (I2maxR)/2. The response curve is also called the selectivity curve of the circuit.

3. Determine the resonant frequency for the specifications: R = 10Ω, L = 0.1H, C = 10µF.
a) 157
b) 158
c) 159
d) 160

Explanation: The frequency at which the resonance occurs is called resonant frequency. The expression of the resonant frequency is given by fr = 1/(2π√LC). On substituting the given values we get resonant frequency = 1/(2π√(0.1×10×10-6))=159.2 Hz.

4. The expression for lower half power frequency is?
a) (-R+√(x2+4LC))/4πL
b) (–R-√(x2+4LC))/4πL
c) (R-√(x2+4LC))/4πL
d) (R+√(x2+4LC))/4πL

Explanation: Selectivity indicates how well a resonant circuit responds to a certain frequency and eliminates all other frequencies. At lower power frequency, XC > XL(1/2πf1C)-2πf1L=R. f1 = (-R+√(x2+4LC))/4πL.

5. The expression for upper half power frequency is?
a) (R+√(x2+4LC))/4πL
b) (R-√(x2+4LC))/4πL
c) (–R-√(x2+4LC))/4πL
d) (-R+√(x2+4LC))/4πL

Explanation: The narrower the bandwidth the greater the selectivity. At upper half power frequency, XC < XL => -(1/2πf2C)+2πf2L=R. f2 = (R+√(x2+4LC))/4πL.
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6. The expression for bandwidth is?
a) R/πL
b) R/2πL
c) R/4πL
d) R/8πL

Explanation: The bandwidth of any system is the range of frequencies for which the current or output voltage is equal to 70.7% of its value at the resonant frequency. The expression of bandwidth is BW = f2 – f1 = R/2πL.

7. In series circuits, the expression for quality factor is?
a) fr
b) BW
c) fr/BW
d) BW/fr

Explanation: The quality factor is the ratio of the reactive power in the inductor or capacitor to the true power in the resistance in series with the coil or capacitor. The expression of quality factor is Q = fr/BW.

8. In a series circuit having resistance and inductance, the quality factor is?
a) ωL/R
b) R/ωL
c) ωL
d) R

Explanation: Quality factor Q = ωL/R. A higher value of circuit Q results in smaller bandwidth and a lower value of Q causes a larger bandwidth.

9. If a series circuit contains resistor and capacitor, the expression for quality factor is?
a) C
b) ωRC
c) ωC
d) 1/ωRC

Explanation: The expression of quality factor is Q = 1/ωRC. The ratio of voltage across either L or C to the voltage applied the resonance can be defined as magnification.

10. The quality factor of the coil for a series circuit having R = 10Ω, L = 0.1H, C = 10µF.
a) 1
b) 5
c) 10
d) 15

Explanation: The resonant frequency is given by fr = 1/(2π√LC)=1/(2π√(0.1×10×10-6))=159.2 Hz. The relation between quality factor, resonant frequency and bandwidth is Q = fr/BW = 2πfrL/R = (6.28×159.2×0.1)/10=10.

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