The current through a $50 - \Omega$ resistor is $I = ( 0.80 \mathrm {~A} ) \sin ( 240 t )$, where $t$ is measured in seconds. What is the rms current?
A) $1.6 \mathrm {~A}$
B) $0.80 \mathrm {~A}$
C) $1.1 \mathrm {~A}$
D) $0.57 \mathrm {~A}$

Question

Quizplus · Accepted Answer

The RMS (root mean square) value of a sinusoidal current $I = I_0 \sin(\omega t)$ is given by $I_{\text{rms}} = \frac{I_0}{\sqrt{2}}$. Here, $I_0 = 0.80 \, \text{A}$, so $I_{\text{rms}} = \frac{0.80 \, \text{A}}{\sqrt{2}} \approx 0.57 \, \text{A}$.

The Current Through A 50−Ω50 - \Omega50−Ω Resistor Is I=(0.80 A)sin⁡(240t)I = ( 0.80 \mathrm {~A} ) \sin ( 240 t )I=(0.80 A)sin(240t)

The Current Through A $50 - \Omega$ Resistor Is $I = ( 0.80 \mathrm {~A} ) \sin ( 240 t )$