Rectangular to Polar form & Polar to Rectangular form conversion

Phasor form conversion is the method of changing the representation form of a phasor. A Phasor is a rotating vector in a complex number form which expresses the magnitude and its phase. Sinusoidal signals with different magnitudes and phases, but the same frequency can be plotted on a phasor diagram; in a phasor diagram, the angular velocity (w) will be the same for all signals.

Phasors play a vital role in the analysis of AC circuits. Because it can be used to express the difference in magnitude and phase of multiple signals or parameters of the same signal. The complex form has two components, that is a real and imaginary part. In a phasor diagram, the real axis lays in the horizontal axis and the imaginary axis in the vertical axis. The phasor can be represented mathematically in three principal forms such as Rectangular form, trigonometrical form and Polar form.

The  Rectangular form is represented by a real part (horizontal axis) and an imaginary (Vertical axis) part of the vector.

convert rectangular to polar

The Polar Form is represented by vector magnitude and angle with respect to the real axis. The vector value will be the modulus of the complex number. The value of the angle is represented either in degrees or radians, which is denoted by θ (Theta).convert polar form to rectangular form calculator

Rectangular to Polar Form Conversion

Rectangular form of a vector, v = a + jb. where a is the real axis value and b is the value of an imaginary axis.

To find the Phasor magnitude V, calculate the modulus of vector a + jb.

Magnitude of vector, V = √ a2 + b2.

To find the angle of a vector with respect to the horizontal axis, θ = tan-1 (b/a).

Phasor form of vector a+jb is, v = V∠θ.

Convert Polar to Rectangular Form

Polar form of the vector, v = V∠θ.

Phasor form of vector a+jb is, v = V∠θ.

To convert to rectangular form, calculate the horizontal and vertical axis values for the vector V.

a = V * cosθ

b = V* sinθ

Rectangular form of vector V∠θ is, v = a+jb.

12 Responses

  1. Narender says:

    j10 polar form

  2. Luc says:

    Hey thank you so much for this, no other online material was making as much sense as this did. So straightforward!

  3. Ryan says:

    convert 5cosθ into polar form and what does θ represent here. What is the relation between θ in 5cosθ and θ1 in 5∠θ1

  4. zae ris says:

    convert 25sin2000t to the polar form . what is the angle ?

  5. akshith says:

    what is the instantaneous value if the rectangular form is a+jb .and angular velocity is W

  6. Rufus says:

    Z= 1/1+j to polar form

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