Subjects electrical engineering

Rectangular To Polar

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Rectangular To Polar


1. The problem is to convert a complex number representing the final node voltage from rectangular form to polar form. 2. Rectangular form of a complex number is given by $z = x + jy$, where $x$ is the real part and $y$ is the imaginary part. 3. Polar form is expressed as $z = r \angle \theta$, where $r$ is the magnitude and $\theta$ is the phase angle. 4. To convert from rectangular to polar form, use the formulas: $$r = \sqrt{x^2 + y^2}$$ $$\theta = \tan^{-1}\left(\frac{y}{x}\right)$$ 5. Calculate the magnitude $r$ by taking the square root of the sum of squares of the real and imaginary parts. 6. Calculate the angle $\theta$ by taking the arctangent of the ratio of the imaginary part to the real part. 7. The angle $\theta$ is usually expressed in degrees or radians depending on the context. 8. This conversion helps in analyzing the voltage magnitude and phase in AC circuit analysis. 9. Example: If the final node voltage is $3 + j4$, then $$r = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$$ $$\theta = \tan^{-1}\left(\frac{4}{3}\right) \approx 53.13^\circ$$ 10. So, the polar form is $5 \angle 53.13^\circ$.