The GATE Grind

GATE 2014 EC (EC3) – Question 16

Networks, Signals and Systems · Time and Frequency Domain Analysis of Linear Circuits · 1 mark · Multiple choice

A series RC circuit connects to DC source at t = 0, with $V_S=Ri(t)+\frac1C\int_0^ti(u)\,du$. Which graph represents i(t)?

Diagram for GATE 2014 EC (EC3) question 16
  1. Graph A
  2. Graph B
  3. Graph C
  4. Graph D

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) Graph A

Explanation

Differentiating the given constant-source equation gives0=Ri′+i/C, so i(t)=i(0+)e^(−t/RC). At0+ the integral is zero, hence i(0+)=Vs/R. Current starts finite and decays exponentially to zero as the capacitor charges, matching **A**.