a$.$ In a frequency modulated $($FM$)$ system, the audio frequency $($AF$)$ is $600$ Hz $,$ and the AF voltage is $2\mathrm{.}5$ V $,$ resulting in a deviation of $5$ kHz $.$ If the AF voltage is increased to $7$ V $,$ determine the new frequency deviation and modulation index for both cases?

b$.$ The FM wave represented by the voltage equation $v=15sin(5{10}^{6}t+20sin2500t).$ Calculate the:

i$.$ Carrier frequency.

ii$.$ Modulating frequency.

iii. Modulation index;

iv$.$ Maximum deviation ; and

v$.$ Power of this FM wave dissipate across a $20$ resistor.