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GATE 2015 EE (EE2) – Question 28

Electric Circuits · Network Elements: Ideal voltage and current sources, dependent sources, R, L, C, M elements · 1 mark · Multiple choice

The series RL circuit has zero initial conditions and a DC source V switched on at t=0. The value of $d^2i/dt^2$ at $0^+$ is

Diagram for GATE 2015 EE (EE2) question 28
  1. $V/L$
  2. $-V/R$
  3. $0$
  4. $-RV/L^2$

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Correct answer: (D) $-RV/L^2$

Explanation

For t>0, L di/dt+Ri=V. Since i(0+)=0, its initial slope is V/L.

Differentiate the equation for positive time: L i″+Ri′=0. Evaluating at 0+ gives i″(0+)=−(R/L)(V/L)=**−RV/L², D**. This is the right-hand ordinary derivative after switching.

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