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![**Problem Statement:**
A current passing through a resistor (\(R = 12 \, \Omega\)) decreases exponentially with time as \(I(t) = I_0 e^{-\alpha t}\) where \(I_0 = 5.5 \, \text{A}\) and \(\alpha = 0.35 \, \text{s}^{-1}\).
**Task 1:**
Calculate the energy dissipated by the resistor in joules during the first \(7\) seconds.
\[ E = \]
**Task 2:**
Calculate the total energy dissipated by the resistor in joules as time goes to infinity.
\[ E(t \to \infty) = \]](https://content.bartleby.com/qna-images/question/8250c86c-ed6e-43af-9ad5-e34c083140fb/bde88056-ad0f-4840-a385-ba47c8d194cf/0mlo16_processed.png)
Transcribed Image Text:**Problem Statement:**
A current passing through a resistor (\(R = 12 \, \Omega\)) decreases exponentially with time as \(I(t) = I_0 e^{-\alpha t}\) where \(I_0 = 5.5 \, \text{A}\) and \(\alpha = 0.35 \, \text{s}^{-1}\).
**Task 1:**
Calculate the energy dissipated by the resistor in joules during the first \(7\) seconds.
\[ E = \]
**Task 2:**
Calculate the total energy dissipated by the resistor in joules as time goes to infinity.
\[ E(t \to \infty) = \]
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