GATE EC 2026 Set 1 — Question 23
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Engineering Mathematics → Differential Equations → Initial & Boundary Value Problems
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Question
The relation between the input current () and the output voltage () of a circuit is governed by the equation: . The circuit is excited by , where is a real valued constant. at is .Which of the following is an equivalent representation of the above case?
Correct answer
(A) C (dV)/(dt) = -m(t), with V(t = 0^-) = V₀ + q/C
Solution
The governing differential equation is:Given , we integrate the equation from to to find the change in voltage due to the impulse:Assuming is a finite signal (no impulses), the integral of over an infinitesimal interval is zero. Thus:For , the impulse , so the equation becomes:This system can be represented by the homogeneous-like equation for with the updated initial condition . Note that the options in the question contain a typographical error using instead of . Option (A) represents the intended equivalent form.
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