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GATE 2026 EE – Question 40

Power Systems · Principles of over-current, differential, directional and distance protection; Circuit breakers · 2 marks · Multiple choice

The operating characteristic of a reactance relay is given by $X\le1\ \Omega$, where $X$ is the reactance calculated by the relay. Its operating characteristic in the admittance plane ($G$-$B$ plane, where $G$ and $B$ denote conductance and susceptance, respectively, expressed in ℧) is given by:

  1. $G^2+(B+0.5)^2\ge\dfrac14$
  2. $B\ge1$
  3. $(G-1)^2+B^2\le\dfrac12$
  4. $G^2+(B-1)^2\ge\dfrac12$

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Show answer and explanation

Correct answer: (A) $G^2+(B+0.5)^2\ge\dfrac14$

Explanation

With $Z=R+jX$, $Y=\dfrac1Z=G+jB$ where $G=\dfrac{R}{R^2+X^2}$ and $B=-\dfrac{X}{R^2+X^2}$. Then $X=-\dfrac{B}{G^2+B^2}$. The condition $X\le1$ gives $-B\le G^2+B^2$, i.e. $G^2+B^2+B\ge0$, which is $G^2+(B+0.5)^2\ge\dfrac14$: the region outside a circle of radius 0.5 centred at $(0,-0.5)$.