Final answer:
The characteristic equation \( |Z+K_4| = (K_1+K_2) \) represents a circle in the R-X plane with its center at the negative of the real and imaginary parts of \( K_4 \) and a radius of \( K_1 + K_2 \).
Step-by-step explanation:
The characteristic equation of an offset impedance relay given by \( |Z+K_4| = (K_1+K_2) \) does indeed describe a circle in the R-X plane where R represents resistance and X represents reactance. To show this, we can start by expressing Z as a complex number Z = R + jX, where R is the real part (resistance) and jX is the imaginary part (reactance), with j representing the imaginary unit.
Now, let's rewrite the characteristic equation as:
\( |(R + jX) + K_4| = K_1 + K_2 \)
Assuming that \( K_4 \) is also a complex number, \( K_4 = a + jb \), the equation becomes:
\( |(R + a) + j(X + b)| = K_1 + K_2 \),
which simplifies to:
\( \sqrt{(R + a)^2 + (X + b)^2} = K_1 + K_2 \).
Squaring both sides we get:
\( (R + a)^2 + (X + b)^2 = (K_1 + K_2)^2 \),
which is the standard form of the equation of a circle with the center at (-a, -b) and the radius equal to \( K_1 + K_2 \).