For multiplication and division of phasors, we use ____________ form.

Question

Examoogle · Accepted Answer

Polar

Explanation: Phasors are complex numbers that represent sinusoidal quantities in steady-state AC circuits. Multiplication and division are most efficiently performed in the polar form because magnitudes are multiplied/divided directly and angles are added/subtracted respectively.

Working Principle: In polar form, a complex number is represented as $M\angle	heta$. For multiplication: $(M_1\angle	heta_1) 	imes (M_2\angle	heta_2) = (M_1 	imes M_2)\angle(	heta_1 + 	heta_2)$. For division: $\frac{M_1\angle	heta_1}{M_2\angle	heta_2} = (\frac{M_1}{M_2})\angle(	heta_1 - 	heta_2)$. This avoids the cumbersome process of converting to rectangular form and performing binomial multiplication or rationalizing denominators.

Key Formulas: $Z_1 Z_2 = (M_1 M_2) \angle (	heta_1 + 	heta_2)$ — Multiplication rule; $\frac{Z_1}{Z_2} = (\frac{M_1}{M_2}) \angle (	heta_1 - 	heta_2)$ — Division rule

Key Points: Polar form uses Magnitude and Angle ($M\angle	heta$).; Rectangular form is preferred for addition and subtraction of phasors.; The transition between polar and rectangular forms uses Euler's Identity: $e^{j	heta} = \cos	heta + j\sin	heta$.

Advantages: Multiplication involves simple arithmetic operations on magnitudes.; Phase angles are combined using simple addition or subtraction.; Reduces computational complexity and probability of calculation errors.

Disadvantages: Does not visually represent the real and imaginary components directly.; Requires conversion if the final result is needed in $a+jb$ format.

Applications: Calculation of power $S = VI^*$.; Determining voltage drops in AC series circuits.; Calculating complex impedance $Z = \frac{V}{I}$.

Additional Info: Rectangular form $a+jb$ is ideal for addition and subtraction because components are summed independently.. Option A is incorrect because rectangular multiplication requires FOIL (First-Outer-Inner-Last) method and rationalization, which is slower.. Always ensure your calculator is in the correct mode (Complex or Polar) during competitive exams.

Answer: B is correct — Polar form is used for multiplication and division because magnitudes multiply/divide and angles add/subtract.

Exam Tip: If you ever have to multiply numbers in rectangular form $a+jb$, it is almost always faster to convert to polar form, perform the operation, and convert back if necessary.

Related Questions

Discussion (0)