# The voltage across an element is

The voltage across an element is $12e^{-2t}$ V. The current entering the positive terminal of the element is $2e^{-2t}$ A. Find the energy absorbed by the element in 1.5 s starting from t = 0.

#### Solution:

The energy absorbed can be found by:

$\,\displaystyle W=\int^{t_2}_{t_1} (v)(i)\,dt$

(Where $W$ is energy absorbed, $v$ is voltage, $t$ is time, and $i$ is current)

Substitute our voltage and current equations:

$\,\displaystyle W=\int^{1.5}_{0} (12e^{-2t})(2e^{-2t})\,dt$

$\,\displaystyle W=\int^{1.5}_{0} (24e^{-4t})\,dt$

$W=\dfrac{24e^{-4t}}{-4}\Big|^{1.5}_{0}$

$W=5.985$ J