physics : class12 Antenna Resonance : Radio Waves : Electromagnetic Waves MCQ Questions and Answers
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Antenna Resonance
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MCQ Questions
1. A thin half-wave dipole antenna is designed to resonate at 150 MHz in free space. Taking the speed of electromagnetic waves as 3.0 × 10^8 m/s, what is its approximate physical length?
A.
0.50 m
B.
1.00 m
C.
1.50 m
D.
2.00 m
Correct Answer:
1.00 m
Explanation:
At resonance, a half-wave dipole has length approximately λ/2. The wavelength is λ = c/f = (3.0 × 10^8)/(150 × 10^6) = 2.0 m, so the antenna length is λ/2 = 1.0 m.
2. An antenna behaves as a resonant circuit with effective inductance 2.0 μH and effective capacitance 20 pF. At what frequency does it resonate?
A.
7.96 MHz
B.
25.2 MHz
C.
79.6 MHz
D.
252 MHz
Correct Answer:
25.2 MHz
Explanation:
Antenna resonance occurs when the inductive and capacitive reactances cancel. Thus, f = 1/(2π√LC) = 1/[2π√((2.0 × 10^-6)(20 × 10^-12))] ≈ 25.2 MHz.
3. A quarter-wave monopole antenna resonates at 75 MHz in air. If the antenna is placed in a medium where the wave speed is 2.4 × 10^8 m/s, what length is required for resonance at the same frequency?
A.
0.40 m
B.
0.80 m
C.
1.20 m
D.
1.60 m
Correct Answer:
0.80 m
Explanation:
The wavelength in the medium is λ = v/f = (2.4 × 10^8)/(75 × 10^6) = 3.2 m. A quarter-wave monopole resonates when its length is λ/4, giving 0.80 m.
4. The effective inductance of a resonant antenna remains constant while its effective capacitance is increased by a factor of four. How does its resonant frequency change?
A.
It becomes four times larger
B.
It becomes twice as large
C.
It becomes half as large
D.
It becomes one-fourth as large
Correct Answer:
It becomes half as large
Explanation:
The resonant frequency of an antenna modeled as an LC circuit is f = 1/(2π√LC). Increasing capacitance by a factor of four increases √C by a factor of two, so the resonant frequency becomes half its original value.
5. A half-wave dipole resonates at 120 MHz. Neglecting end effects, which frequency corresponds to its next higher odd-mode resonance?
A.
180 MHz
B.
240 MHz
C.
360 MHz
D.
480 MHz
Correct Answer:
360 MHz
Explanation:
For a dipole of fixed length, resonant frequencies occur approximately when its length equals λ/2, 3λ/2, 5λ/2, and so on. The next higher odd mode is the third-harmonic resonance, so its frequency is 3 × 120 MHz = 360 MHz.
6. At resonance, the input impedance of an ideal series-equivalent antenna circuit is purely resistive. If its effective resistance is 50 Ω and the applied radio-frequency voltage is 10 V rms, what is the rms current at resonance?
A.
0.05 A
B.
0.10 A
C.
0.20 A
D.
0.50 A
Correct Answer:
0.20 A
Explanation:
At antenna resonance, the inductive and capacitive reactances cancel, leaving only the resistance. Therefore, I = V/R = 10/50 = 0.20 A.
7. A resonant antenna has quality factor Q = 80 and resonant frequency 160 MHz. Using the approximate relation Q = f0/Δf, what is its resonance bandwidth?
A.
0.50 MHz
B.
1.0 MHz
C.
2.0 MHz
D.
12.8 MHz
Correct Answer:
2.0 MHz
Explanation:
The resonance bandwidth is Δf = f0/Q = 160 MHz/80 = 2.0 MHz. A higher Q would correspond to a narrower resonant frequency range.
8. A half-wave dipole antenna has a resonant length of 1.5 m at 100 MHz. To make the same antenna resonate at 125 MHz, what approximate physical length should be used, assuming the wave speed and end effects remain unchanged?
A.
0.80 m
B.
1.20 m
C.
1.50 m
D.
1.875 m
Correct Answer:
1.20 m
Explanation:
For a fixed mode, the resonant antenna length is inversely proportional to frequency because L ≈ λ/2 = c/(2f). Thus, L2 = L1(f1/f2) = 1.5 × (100/125) = 1.20 m.
9. An antenna is exactly resonant at 90 MHz. Its effective inductance is unchanged, but a nearby object increases its effective capacitance by 21%. Approximately what is the new resonant frequency?
A.
75 MHz
B.
81 MHz
C.
99 MHz
D.
109 MHz
Correct Answer:
81 MHz
Explanation:
Since f is proportional to 1/√C, the new frequency is f' = 90/√1.21 = 90/1.1 ≈ 81 MHz. The increased capacitance shifts the antenna resonance to a lower frequency.
10. A straight antenna of fixed length resonates in its fundamental mode at 60 MHz. Ignoring end effects, at which frequency will it resonate when operated in the next allowed odd mode?
A.
90 MHz
B.
120 MHz
C.
180 MHz
D.
240 MHz
Correct Answer:
180 MHz
Explanation:
For a straight dipole, the fundamental and successive odd-mode resonances correspond approximately to lengths λ/2, 3λ/2, 5λ/2, and so forth. The next allowed odd mode is the third harmonic, whose frequency is 3 × 60 MHz = 180 MHz.
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