For an amplitude modulated wave, the maximum amplitude is found to be 10 V while the minimum amplitude is found to be 2 V. The modulation index is

Given, maximum amplitude A_max = 10 V

Minimum amplitude A_min = 2 V

Let A_c and A_m be the amplitudes of carrier wave and signal wave

∴   A_max = A_c + A_m = 10   ...(i)

and   A_min = A_c – A_m = 2   ...(i)

Adding the Eqs. (i) and (ii), we get

2A_c = 12

or  A_c = 6 V

and  A_m = 10 – 6 = 4 V

 $\mu =\frac{A_m}{A_c}=\frac{4}{6}=\frac{2}{3}$