When a broadcast AM transitor is 50% modulated, its antenna current is 12A. What would be the carrier current ?

Explanation

Antenna current = `I_(t) = 12 A`
`m = (50)/(100) = (1)/(2)`
Carrier current ` = I_(c) = ?`
`I_(c) = (I_(t))/(sqrt(1+(m^(2))/(2)))`
` I_(c) = (12)/(sqrt(1+(1)/(2)((1)/(2))^(2))) = (12)/(sqrt(1+(1)/(8)))`
` = (12)/(sqrt(918)) = (12)/(sqrt(1+(1)/(8)))`
`= (12)/(sqrt(918)) = (12sqrt(8))/(sqrt(9))`
` = (12 xx 2 sqrt(2))/(3) = 8sqrt(2) = 8 xx 1.414`
` = 11.3 A`