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This set of Antennas MCQs focuses on “Radiation – Hertzian Dipole”.

1. Hertzian dipole carries which type of current throughout its length while radiating?
a) Varying
b) Constant
c) Depends on type of polarization

Explanation: Hertzian dipole is a short linear antenna which carries a constant current throughout its length while radiating. It consists of two equal and opposite charges separated by a very short distance. It is infinitesimal current element.

2. Power radiated by a Hertzian dipole of length λ/30 and carrying a current 2A?
a) 0.87W
b) 3.51W
c) 2.51W
d) 8.77W

Rrad = $$80\pi^2(\frac{l}{\lambda})^2=80\pi^2(\frac{\frac{\lambda}{30}}{\lambda})^2=0.877\Omega$$

3. A Hertzian dipole consists of two _____ and ______ charges separated by a very short distance.
a) unequal, opposite
b) equal, same
c) equal, opposite
d) unequal, same

Explanation: A Hertzian dipole consists of two equal and opposite charges separated by a very short distance. It is infinitesimal current element. It is a short linear antenna which carries a constant current throughout its length while radiating.
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4. When Hertzian dipole is connected to a practical antenna, which of the following fields is observed to be absent when a uniform current flow is observed?
b) Induction field
c) Electrostatic field
d) Both radiation and Induction Field

Explanation: Since a constant current flow and there is no any charge accumulation at the ends of the dipole, the term 1/r3disappears. Therefore, electrostatic field is absent.

5.Which of the following is the radiation resistance of the Hertzian dipole?
a) $$\frac{\eta_0 w^2 dl^2}{6\pi c^2}$$
b) $$\frac{\eta_0 wdl^2}{6\pi c^2}$$
c) $$\frac{\eta_0 w^2 dl^2}{3\pi c^2}$$
d) $$\frac{\eta_0 w^3 dl^2}{3\pi c^3}$$

Explanation: Radiation resistance of a Hertzian dipole is $$R_{rad} = 80\pi^2(\frac{l}{\lambda})^2$$
By simplifying the options given above,
$$\frac{\eta_0 w^2 dl^2}{6\pi c^2} = \frac{120\pi(2\pi/\lambda)^2 dl^2}{6\pi} = 80\pi^2(\frac{l}{\lambda})^2$$

6. If the radiation resistance of a Hertzian dipole is 100Ω, then the radiation resistance of short dipole is ____Ω.
a) 25
b) 50
c) 73
d) 35.6

Explanation: The radiation resistance of the short dipole is ¼ times the radiation resistance of a current element. So 100/4= 25Ω.

7. The radiation resistance of a monopole of height 1cm and operating at frequency 100MHz is ____ Ω.
a) 4.83m
b) 4.38k
c) 4.38m
d) 4.83k

Explanation: The radiation resistance of a monopole is 1/8 times the current element.
$$R_{rad}=10\pi^2 (l/\lambda)^2$$
For a monopole height h= l/2 => l= 2h
$$R_{rad}=10\pi^2(\frac{2h}{\lambda})^2=40\pi^2 (\frac{hf}{c})^2=40\pi^2 (\frac{1×100×10^6}{3×10^{10} })^2=4.38m\Omega$$

8. The radiation resistance of a monopole is _____ times the current element.
a) 1/8
b) 1/4
c) 1/2
d) 1/16

Explanation: The radiation resistance of monopole is ½ times the short dipole. But the radiation resistance of short dipole is ¼ time the current element.
$$R_{rad \,mono}=\frac{1}{2}×\frac{1}{4}×80\pi^2(\frac{l}{\lambda})^2=\frac{1}{8}×80\pi^2(\frac{l}{\lambda})^2=10\pi^2 (\frac{l}{\lambda})^2=\frac{R_{rad \,Herztian}}{8}$$
The radiation resistance of monopole is 1/8 times the current element.

9. Practically we don’t use Hertzian dipole.
a) True
b) False

Explanation: Since the current distribution at the center is maximum and minimum at ends, there is no uniform distribution of current along length. But Hertzian dipole is derived by assuming a uniform current distribution along length and having infinitesimal length. So that is reason why we don’t use Hertzian dipole practically.

10. If the radiation resistance of a monopole is 18Ω, then the radiation resistance of a Hertzian dipole is _____________
a) 124Ω
b) 144Ω
c) 164Ω
d) 154Ω

Explanation: The radiation resistance of monopole is 1/8 times the current element.