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
\,\displaystyle W=\int^{1.5}_{0} (24e^{-4t})\,dt
W=\dfrac{24e^{-4t}}{-4}\Big|^{1.5}_{0}
W=5.985 J