Numerial - Change in transmission power with change in modulation index

What is the effect on the transmitted power of AM signal when the modulation index changes from 0.8 to 1?

a.) 0.1364
b.) 0.3856
c.) 1.088
d.) 0.5

Correct Answer : a.) 0.1364

Explanation:

The total power in an AM is given by
P_t= P_c ( 1 + m²/2)
Where P_c is the carrier power and m is the modulation index.

Therefore,

P_t1 = P_c ( 1 + 0.8²/2) = 1.32 P_c
P_t2 = P_c ( 1 + 1²/2) = 1.5 P_c
Increase in power = (1.5 P_c - 1.32 P_c)/ 1.32 P_c
= 0.1364