Choose the one alternative that best completes the statement or answers the question.
-The current I, in amperes, flowing through a particular ac (alternating current) circuit at time t seconds is $$I = 220 \sin ( 65 \pi t )$$ What is the period and amplitude of the current?
A) period $= \frac { \pi } { 120 }$ second, amplitude $= 60$
B) period $= \frac { 1 } { 30 }$ second, amplitude $= 120$
C) period $= 60 \pi$ seconds, amplitude $= \frac { 1 } { 30 }$
D) period $= \frac { 1 } { 480 }$ second, amplitude $= 480$

Question

Choose the one alternative that best completes the statement or answers the question.
-The current I, in amperes, flowing through a particular ac (alternating current) circuit at time t seconds is $$I = 220 \sin ( 65 \pi t )$$ What is the period and amplitude of the current? 
A) period $= \frac { \pi } { 120 }$ second, amplitude $= 60$
B) period $= \frac { 1 } { 30 }$ second, amplitude $= 120$
C) period $= 60 \pi$ seconds, amplitude $= \frac { 1 } { 30 }$
D) period $= \frac { 1 } { 480 }$ second, amplitude $= 480$

Quizplus · Accepted Answer

The amplitude of the current is the coefficient of the sine function, which is 220. The period of a sine function is given by $ \frac{2\pi}{\omega} $, where $ \omega $ is the angular frequency. Here, $ \omega = 65\pi $, so the period is $ \frac{2\pi}{65\pi} = \frac{1}{32.5} $, which simplifies to $ \frac{2}{65} $ or $ \frac{1}{32.5} $, which is approximately $ \frac{1}{30} $ second. Therefore, the correct answer is the one that lists the amplitude as 220 (none of the options do, but it seems there's a mistake in the question or answer choices as they don't match the amplitude given in the question) and the period closest to $ \frac{1}{30} $ second.

Choose the One Alternative That Best Completes the Statement or Answers