Question
Download Solution PDFThe total charge q(t), in the coulombs, that enters the terminal of an element is:
\(q(t) = \left\{ {\begin{array}{*{20}{c}} {0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,t < 0}\\ {2t\,\,\,\,\,\,\,\,\,\,\,\,0 \le t \le 2}\\ {3 + {e^{ - 2(t - 2)}}\,\,t > 2} \end{array}} \right.\)
Determine the current at t = 5 s.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Electric Current: Electric current may be defined as the time rate of net motion of an electric charge across a cross-sectional boundary.
Electric current , i = Rate of transfer of electric charge.
i (t) = \(\frac{{dQ}}{{dt}}\)
Calculation:
t = 5 s so, equation 3rd is consider.
\(i = \frac{{dQ}}{{dt}} = \frac{d}{{dt}}\left( {3 + {e^{ - 2\left( {t - 2} \right)}}} \right)\)
\(i = {e^{ - 2\left( {t - 2} \right)}}\frac{d}{{dt}}\left[ { - 2\left( {t - 2} \right)} \right]\)
\(i = {e^{ - 2\left( {t - 2} \right)}}\left( { - 2} \right)\)
\(i = - 2{e^{ - 2\left( {t - 2} \right)}}\)
Put the value of t = 5, then we get,
\(i = - 2{e^{ - 6}}\;A\;\)
Last updated on Jul 1, 2025
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