Solve the equation for exact solutions.
-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, i is the maximum current, and t is the time in seconds. Solve the equation for t.
A) $t = 2 \pi f \cos \left( - \frac { 2 \pi f V c } { i } \right)$

B) $t = 2 \pi f \arccos \left( - \frac { 2 \pi \mathrm { fVc } } { \mathrm { i } } \right)$

C) $\mathrm { t } = \frac { 1 } { 2 \pi \mathrm { f } } \arccos \left( \frac { 2 \pi \mathrm { fVc } } { \mathrm { i } } \right)$

D) $t = \frac { 1 } { 2 \pi f } \arccos \left( - \frac { 2 \pi f V c } { i } \right)$

Question

Solve the equation for exact solutions.
-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, i is the maximum current, and t is the time in seconds. Solve the equation for t. 
A) $t = 2 \pi f \cos \left( - \frac { 2 \pi f V c } { i } \right)$

B) $t = 2 \pi f \arccos \left( - \frac { 2 \pi \mathrm { fVc } } { \mathrm { i } } \right)$

C) $\mathrm { t } = \frac { 1 } { 2 \pi \mathrm { f } } \arccos \left( \frac { 2 \pi \mathrm { fVc } } { \mathrm { i } } \right)$

D) $t = \frac { 1 } { 2 \pi f } \arccos \left( - \frac { 2 \pi f V c } { i } \right)$

Quizplus · Accepted Answer

To solve for $t$, we isolate $t$ in the equation given. Starting with $V_C = - \frac{i}{2\pi f} \cos 2\pi ft$, we first multiply both sides by $-\frac{2\pi f}{i}$ to isolate the cosine term, giving $\cos 2\pi ft = -\frac{2\pi fV_C}{i}$. Then, to solve for $t$, we apply the inverse cosine ($\arccos$) to both sides, resulting in $2\pi ft = \arccos\left(-\frac{2\pi fV_C}{i}\right)$. Finally, dividing both sides by $2\pi f$ gives $t = \frac{1}{2\pi f} \arccos\left(-\frac{2\pi fV_C}{i}\right)$, which matches option D.

Solve the Equation for Exact Solutions VC=−i2πfcos⁡2πftV _ { C } = - \frac { i } { 2 \pi f } \cos 2 \pi f tVC​=−2πfi​cos2πft

Solve the Equation for Exact Solutions $V _ { C } = - \frac { i } { 2 \pi f } \cos 2 \pi f t$