ISRO EC 2025 Q.48: solution and answer

ISRO 2025 · ECQ.48 · 1 mark · MCQ

The radiation resistance of an antenna is 63 ohms and the loss resistance is 7 ohms. If antenna has power gain of 16, then directivity is

(A)
48.26 dB
(B)
12.5 dB
(C)
17.77 dB
(D)
24.7 dB

See the question in the paper

Tap to open full size

Answer and solution

ANSWER

The directivity is about 12.5 dB (option B).

Official answer: BSource: ISRO's final answer key of 15 May 2026

Radiation efficiency: $η = \frac{R _{r}}{R _{r} + R _{L}} = \frac{63}{63 + 7} = \frac{63}{70} = 0.9$ .
Power gain and directivity are related by $G = η D$ , so $D = \frac{G}{η}$ .
The gain is given as a plain ratio, $G = 16$ , so $D = \frac{16}{0.9} \approx 17.78$ (a ratio).
Convert to decibels: $D_{dB} = 10 lo g_{10} (17.78) \approx 10 \times 1.25 = 12.5 dB$ .
Option (c), $17.77$ , is the directivity as a pure ratio, so it is not a value in dB. Only option (b), $12.5 dB$ , matches the directivity expressed in decibels.

KEY IDEA

Gain includes the ohmic losses and directivity does not, so $G = η D$ with $η = R_{r} / (R_{r} + R_{L})$ . Find $D$ as a ratio first, then convert to dB.

WATCH OUT FOR

Stopping at the ratio 17.78 and picking the option 17.77 without converting to dB, or treating 16 as a value in dB and adding the efficiency correction in the wrong direction.

From the ISRO EC 2025 paper. Every question of this paper · The full paper (PDF, ISRO) · All 4 ISRO Antennas questions, with notes

ISRO EC 2025 Q.48: solution and answer

Answer and solution

More ISRO Antennas questions