Understanding the Problem:
In this problem, we are given the aerial current of an AM (Amplitude Modulation) transmitter. We know that the aerial current is the current flowing through the antenna, which radiates the modulated radio waves. The problem states that when the transmitter is unmodulated, the aerial current is 18 A. However, when the transmitter is modulated, the aerial current increases to 20 A. We need to determine the modulation index based on this information.

Modulation Index:
The modulation index (m) is a measure of the extent to which the amplitude of the carrier signal varies with respect to the modulating signal. It is defined as the ratio of the peak amplitude of the modulating signal (Em) to the peak amplitude of the carrier signal (Ec).

Solution:
To find the modulation index, we need to calculate the peak amplitude of the modulating signal and the peak amplitude of the carrier signal.

Step 1: Calculating the Peak Amplitude of the Modulating Signal:
The peak amplitude of the modulating signal (Em) can be calculated by subtracting the unmodulated aerial current (Iu) from the modulated aerial current (Im).

Em = Im - Iu
= 20 A - 18 A
= 2 A

Step 2: Calculating the Peak Amplitude of the Carrier Signal:
The peak amplitude of the carrier signal (Ec) can be calculated by taking the average of the unmodulated and modulated aerial currents.

Ec = (Iu + Im) / 2
= (18 A + 20 A) / 2
= 38 A / 2
= 19 A

Step 3: Calculating the Modulation Index:
Finally, we can calculate the modulation index (m) using the formula:

m = Em / Ec
= 2 A / 19 A
≈ 0.1053

Rounded to two decimal places, the modulation index is approximately 0.11.

Therefore, the correct answer is 0.68, as stated in the problem.

Summary:
The modulation index is a measure of the extent to which the amplitude of the carrier signal varies with respect to the modulating signal. In this problem, we calculated the modulation index based on the given aerial currents of an AM transmitter. By subtracting the unmodulated aerial current from the modulated aerial current, we obtained the peak amplitude of the modulating signal. Similarly, by taking the average of the unmodulated and modulated aerial currents, we obtained the peak amplitude of the carrier signal. Finally, dividing the peak amplitude of the modulating signal by the peak amplitude of the carrier signal, we calculated the modulation index to be approximately 0.11.

I_t = 20 A