GATE 2015 EE (EE2) – Question 38

For −10<t<10, $di/dt-0.2i=0$. If i(4)=10, find i(−5).

Show answer and explanation

Correct answer: 1.6 to 1.7

Explanation

The solution is i(t)=Ce⁰·²ᵗ. It is convenient to anchor it at the given time: i(t)=10e⁰·²⁽ᵗ⁻⁴⁾.

At t=−5, the time difference is −9, giving **i(−5)=10e⁻¹·⁸≈1.65299**, within 1.6–1.7. Both times lie within the equation's stated domain.

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