An alternating current takes 3.375ms to reach 15A for the first time after becoming instantaneously zero. The frequency of the current is 40Hz. Find the maximum value of the alternating current.

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written 8.4 years ago by

teamques10 ★ 68k

• modified 4.6 years ago

basic electrical engineering

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written 8.4 years ago by

teamques10 ★ 68k

• modified 8.4 years ago

$i=I_m \sin 2 \pi ft \\ f=40 Hz \\ i=15A$

t $=3.375 ms \\ =3.375\times10^{-3}s$

$i=I_m \sin 2 \pi ft$

15 $=I_m \sin(2 \times \pi\times40\times3.3375\times 10^{-3}) \\ =I_m \sin\bigg[2 \times \pi \times 40 \times 3.375 \times 10^{-3}\times \dfrac{180}{\pi}\bigg]^0$

$15=I_m \sin[48.6]^0 \\ I_m=\dfrac{15}{\sin[48.6]^0} \\ \therefore I_m=20A$

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