$$\text { The current through a capacitor with capacitance of } 33 \mu \mathrm { F } \text { is given by }$$ $$i ( t ) = \left\{ \begin{array} { c }
0.005 e ^ { - 1000 ( - t + 0.003 ) } , \quad 0 \leq t

Question

$$\text { The current through a capacitor with capacitance of } 33 \mu \mathrm { F } \text { is given by }$$ $$i ( t ) = \left\{ \begin{array} { c } 
0.005 e ^ { - 1000 ( - t + 0.003 ) } , \quad 0 \leq t < 0.003 \
0.005 e ^ { - 1000 ( t - 0.003 ) } , \quad 0.003 \leq t < 0.006 \mathrm {~A} \
0 , \quad \text { otherwise }
\end{array} \right.$$ $$\text { Find the voltage across the capacitor } v ( t ) \text { and plot the current and voltage as a function of time. }$$

Quizplus · Accepted Answer

The Answer is

v ( t ) = \frac { 1 } { C } \int _ { 0 } ^ { t } i ( \lambda ) d \lambda = \left\{ \begin{array} { c } 0.007543495 \mathrm { e } ^ { 1000 t } - 0.007543495 , \quad 0 \leq t < 0.003 \0.2954868 - 3.043263 \mathrm { e } ^ { - 1000 t } , 0.003 \leq t < 0.006 \0.2879 , \quad 0.006 \leq t\end{array} \quad \mathrm {~V} ight.

$v ( t ) = \frac { 1 } { C } \int _ { 0 } ^ { t } i ( \lambda ) d \lambda = \left\{ \begin{array} { c } 0.007543495 \mathrm { e } ^ { 1000 t } - 0.007543495 , \quad 0 \leq t < 0.003 \ 0.2954868 - 3.043263 \mathrm { e } ^ { - 1000 t } , 0.003 \leq t < 0.006 \ 0.2879 , \quad 0.006 \leq t \end{array} \quad \mathrm {~V} ight.$
$v ( t ) = \frac { 1 } { C } \int _ { 0 } ^ { t } i ( \lambda ) d \lambda = \left\{ \begin{array} { c } 0.007543495 \mathrm { e } ^ { 1000 t } - 0.007543495 , \quad 0 \leq t < 0.003 \ 0.2954868 - 3.043263 \mathrm { e } ^ { - 1000 t } , 0.003 \leq t < 0.006 \ 0.2879 , \quad 0.006 \leq t \end{array} \quad \mathrm {~V} ight.$

The current through a capacitor with capacitance of 33μF is given by \text { The current through a capacitor with capacitance of } 33 \mu \mathrm { F } \text { is given by } The current through a capacitor with capacitance of 33μF is given by

$\text { The current through a capacitor with capacitance of } 33 \mu \mathrm { F } \text { is given by }$