For addition and subtraction of phasors, we use the _________ form.

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Examoogle · Accepted Answer

Rectangular

Explanation: Phasors in rectangular form are represented as $Z = R + jX$, which allows for simple algebraic addition and subtraction of real and imaginary components independently. While polar form $(Z = |Z|\angle	heta)$ is convenient for multiplication and division, it is not suitable for direct addition because the magnitudes and angles do not combine linearly.

Working Principle: When adding two phasors $A = a_1 + jb_1$ and $B = a_2 + jb_2$, the sum is simply $(a_1 + a_2) + j(b_1 + b_2)$. This component-wise addition leverages the linearity of the complex plane, whereas polar forms must first be converted to rectangular form via $a = |Z|\cos(	heta)$ and $b = |Z|\sin(	heta)$ to perform the operation.

Key Formulas: $Z_{total} = (R_1 + R_2) + j(X_1 + X_2)$ — Addition in rectangular form; $Z = |Z|(\cos	heta + j\sin	heta)$ — Conversion to rectangular form

Key Points: Rectangular form is ideal for addition and subtraction due to independent real/imaginary component processing.; Polar form is ideal for multiplication and division of phasors.; Conversion between forms is necessary if data is provided in mixed formats.; The operator 'j' represents a $90^\circ$ phase shift in the complex plane.

Advantages: Simplifies algebraic addition and subtraction; Direct compatibility with circuit laws like Kirchhoff's Voltage and Current Laws

Disadvantages: Difficult to visualize magnitude and phase angle at a glance; Requires conversion from polar form if values are given as magnitude/angle

Applications: Solving Series and Parallel AC circuits; Nodal and Mesh analysis in AC power systems

Additional Info: In polar form, $Z_1\angle	heta_1 + Z_2\angle	heta_2 
eq (Z_1+Z_2)\angle(	heta_1+	heta_2)$. This is a common student error.. Option B (Polar) is efficient only for products or quotients of phasors because magnitudes multiply and angles add.

Answer: A is correct — The rectangular form, $R + jX$, allows for the direct addition or subtraction of real and imaginary parts, making it the standard for circuit analysis operations involving summation.

Exam Tip: Always ensure your calculator is in the correct mode (Complex mode) when performing these operations, and remember to convert polar coordinates to rectangular before summing series impedances.

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