Solve.
-In the study of alternating electric current, capacitive voltage is given by $V c = - \frac { i } { 2 \pi f } \cos 2 \pi f t$, where $f$ is the number of cycles per second, $\mathrm { i }$ is the maximum current, and $\mathrm { t }$ is the time in seconds. Solve the equation for t.
A) $t = 2 \pi f \operatorname { Arccos } \left( - \frac { 2 \pi \mathrm { fV } _ { \mathrm { C } } } { \mathrm { i } } \right)$
B) $t = 2 \pi f \cos \left( - \frac { 2 \pi \mathrm { fV } _ { \mathrm { C } } } { \mathrm { i } } \right)$
C) $ t=\frac{1}{2 \pi f} \operatorname{Arccos}\left(\frac{2 \pi \mathrm{fV}_{\mathrm{C}}}{i}\right) $
D) $t = \frac { 1 } { 2 \pi f } \operatorname { Arccos } \left( - \frac { 2 \pi \mathrm { fV } _ { \mathrm { C } } } { \mathrm { i } } \right)$

Question

Quizplus · Accepted Answer

To solve for $t$, we isolate $t$ from the equation $V_c = - \frac { i } { 2 \pi f } \cos 2 \pi f t$. Rearranging and solving for $t$ involves taking the arccosine of both sides, leading to $t = \frac { 1 } { 2 \pi f } \operatorname { Arccos } \left( - \frac { 2 \pi \mathrm { fV } _ { \mathrm { C } } } { \mathrm { i } } \right)$.

Solve -In the Study of Alternating Electric Current, Capacitive Voltage Vc=−i2πfcos⁡2πftV c = - \frac { i } { 2 \pi f } \cos 2 \pi f tVc=−2πfi​cos2πft

Solve
-In the Study of Alternating Electric Current, Capacitive Voltage $V c = - \frac { i } { 2 \pi f } \cos 2 \pi f t$