Alternating current in an AC circuit varies with time as i(t) = 100 sin 50πt cos 50πt. The maximum current and frequency are respectively (i is in ampere and t is in second)

Question

Alternating current in an AC circuit varies with time as i(t) = 100 sin 50πt cos 50πt. The maximum current and frequency are respectively (i is in ampere and t is in second) (A) 100 A, 100 Hz (B) 50 √ 2 A, 100 Hz (C) 50 A, 50 Hz (D) 50 A, 100 Hz

Tardigrade Admin · Accepted Answer

i(t) = 100 sin 50π t cos 50π t = 50(2sin 50π t cos 50π t) = 50 sin(100 π t) Io = 50 A and f =(100 π/2π)=50 Hz

Q. Alternating current in an AC circuit varies with time as i(t) = 100 sin 50 $π$ t cos 50 $π$ t. The maximum current and frequency are respectively (i is in ampere and t is in second)

$100 A, 100 Hz$

$502 A, 100 Hz$

$50 A, 50 Hz$

$50 A, 100 Hz$

$i (t) = 100 s in 50 π t cos 50 π t$
$= 50 (2 s in 50 π t cos 50 π t)$
$= 50 s in (100 π t)$
$I_{o} = 50 A an d f = \frac{100 π}{2 π} = 50 Hz$

Q. Alternating current in an AC circuit varies with time as i(t) = 100 sin 50πt cos 50πt. The maximum current and frequency are respectively (i is in ampere and t is in second)

100A,100Hz

502​A,100Hz

50A,50Hz

50A,100Hz