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GATE 2015 EE - SET 2 - Question 28

Solution:

\frac{di}{dt} -0.2i = 0
\frac{1}{i}\frac{di}{dt}=0.2
\int \frac{1}{i}di = \int 0.2dt

ln(i) = 0.2t + c

i = e^{0.2t} + c
i = e^{0.2t} * e^{c}
i = e^{0.2t} * C_{1} --------(1)
i(4) = 10 \Rightarrow i = 10 ; t = 4

10 = e^{0.2(4)} * C_{1}
C_{1} = 10 e^{-0.8}

i = e^{0.2t} * C_{1}
i = e^{0.2t}* 10e^{-0.8}
i = 10e^{0.2t-0.8}---------(2)

i(-5) \Rightarrow t = -5 into (2)

i(-5) = 10 e^{0.2(-5)} - 0.8 = 10 e ^{-1-0.8} =10 e^{-1.8}=1.653

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