Question

An AM transmitter is coupled to an aerial. The input current is found to be \(5\ \text{A}\). With modulation, the current value increases to \(5.9\ \text{A}\). The depth of modulation is:

• A. \(83.4\%\)
• B. \(88.6\%\)
• C. \(78.2\%\)
• D. \(62.6\%\)

Hint:

Use \(I_t = I_c\sqrt{1+m^2/2}\) and solve for \(m\) from the current ratio.

Answer 1

The Correct Option is B

Modulation adds power to the sidebands, so the antenna current climbs above its unmodulated value. The link is $I_t = I_c\sqrt{1 + m^{2}/2}$, where $m$ is the modulation depth.

Rearrange to isolate $m$:
\[m = \sqrt{2\left[\left(\frac{I_t}{I_c}\right)^{2} - 1\right]}.\]

Insert the data $I_t = 5.9\ \text{A}$ and $I_c = 5\ \text{A}$, so $I_t/I_c = 1.18$ and its square is $1.3924$:
\[m = \sqrt{2(1.3924 - 1)} = \sqrt{2 \times 0.3924} = \sqrt{0.7848} = 0.886.\]

Expressed as a percentage this is roughly $88.6\%$, matching option (B). \[\boxed{m \approx 88.6\%}\]