# Electromagnetic Theory Questions and Answers – Input and Characteristic Impedances

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This set of Electromagnetic Theory Multiple Choice Questions & Answers (MCQs) focuses on “Input and Characteristic Impedances”.

1. The characteristic impedance of a quarter wave transformer with load and input impedances given by 30 and 75 respectively is
a) 47.43
b) 37.34
c) 73.23
d) 67.45

Explanation: In quarter wave transformer, the characteristic impedance will be the geometric mean of the input impedance and the load impedance. Thus Zo2 = ZIN ZL. On substituting for ZIN = 75 and ZL = 30, we get the characteristic impedance as 47.43 units.

2. The input impedance of a quarter wave line 50 ohm and load impedance of 20 ohm is
a) 50
b) 20
c) 1000
d) 125

Explanation: The characteristic impedance will be the geometric mean of the input impedance and the load impedance. Thus Zo2 = Zin ZL. On substituting for Zo = 50 and ZL = 20, we get the input impedance as 502/20 = 125 ohm.

3. For a matched line, the input impedance will be equal to
b) Characteristic impedance
c) Output impedance
d) Zero

Explanation: A matched line refers to the input and characteristic impedance being the same. In such condition, maximum transmission will occur with minimal losses. The reflection will be very low.

4. The reflection coefficient lies in the range of
a) 0 < τ < 1
b) -1 < τ < 1
c) 1 < τ < ∞
d) 0 < τ < ∞

Explanation: The reflection coefficient lies in the range of 0 < τ < 1. For full transmission, the reflection will be zero. For no transmission, the reflection will be unity.

5. When the ratio of load voltage to input voltage is 5, the ratio of the characteristic impedance to the input impedance is
a) 1/5
b) 5
c) 10
d) 25

Explanation: From the transmission line equation, the ratio of the load voltage to the input voltage is same as the ratio of the characteristic impedance to the input impedance. Thus the required ratio is 5.

6. The power of the transmitter with a radiation resistance of 12 ohm and an antenna current of 3.5A is
a) 147
b) 741
c) 174
d) 471

Explanation: The power in a transmitter is given by Prad = Iant2 Rrad. On substituting Irad = 3.5 and Rrad =12, we get Prad = 3.52 x 12 = 147 units.

7. The group delay of the wave with phase constant of 62.5 units and frequency of 4.5 radian/sec is
a) 13.88
b) 31.88
c) 88.13
d) 88.31

Explanation: The group delay is given by td = β/ω. Given that β = 62.5 and ω = 4.5, we get the group delay as td = 62.5/4.5 = 13.88 units.

8. The maximum impedance of a transmission line 50 ohm and the standing wave ratio of 2.5 is
a) 20
b) 125
c) 200
d) 75

Explanation: The maximum impedance of a line is given by Zmax = SZo. On substituting for S = 2.5 and Zo = 50, we get Zmax = 2.5 x 50 = 125 ohm.

9. The minimum impedance of a transmission line 75 ohm with a standing wave ratio of 4 is
a) 75
b) 300
c) 18.75
d) 150

Explanation: The minimum impedance of a line is given by Zmin = Zo/S. On substituting for Zo = 75 and S = 4, we get Zmin = 75/4 = 18.75 units.

10. The average power in an electromagnetic wave is given by
a) propagation constant
b) poynting vector
c) phase constant
d) attenuation constant

Explanation: The Poynting vector is the cross product of the electric field and magnetic field intensities. It gives the total power of an electromagnetic wave.

11. The characteristic impedance of a transmission line is normally chosen to be
a) 50
b) 75
c) 50 or 75
d) 100

Explanation: The characteristic impedance is always 50 ohm or 75 ohm for a transmission line. This is because of the GHz range of operation and the load impedences employed.

12. Identify the material which is not present in a transmission line setup.
a) waveguides
b) cavity resonator
c) antenna
d) oscillator

Explanation: The transmission line setup consists of antennae for transmitting and receiving power. It consists of waveguides and cavity resonator for guided transmission of electromagnetic waves. Thus oscillator is the odd one out.

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