A parallel circuit consists of two branches: one with impedance (4 + j3) Ω and another with (4 − j3) Ω connected to 100 V supply. Then1.The total impedance is purely resistive.2.The equivalent impedance magnitude is 4 Ω.3.Total current drawn is 25 A.4.Power factor of circuit is unity.Which of the above statements is/are correct?

Correct Answer: B - 1 and 4 only

Quick Concept Explanation

The equivalent resistance is not simply R; it is obtained after adding the two admittances. Complex-conjugate multiplication gives |4+j3|²=25. Adding admittances cancels ±j3/25 exactly. Key relation: Yeq = 1/(4+j3)+1/(4−j3)=8/25=0.32 S; Zeq=1/Yeq=3.125 Ω; I=V/Zeq=32 A; PF=cos0°=1.

Exam focus: For parallel complex branches, convert Z to Y first; it prevents sign and denominator mistakes. Common trap: Directly adding parallel impedances or assuming the equivalent resistance equals the real part of each branch.

Statement-wise Verification

• Statement 1 - Correct.
  The total impedance is purely resistive.
  The imaginary parts cancel in admittance because the branch impedances are complex conjugates.
• Statement 2 - Incorrect.
  The equivalent impedance magnitude is 4 Ω.
  The equivalent magnitude is 3.125 Ω, not 4 Ω.
• Statement 3 - Incorrect.
  Total current drawn is 25 A.
  I = 100/3.125 = 32 A, not 25 A.
• Statement 4 - Correct.
  Power factor of circuit is unity.
  Equivalent impedance is purely real, so the phase angle is zero and power factor is 1.

Core Concept

Parallel AC impedances should be combined through admittance. For conjugate branches R+jX and R−jX, their susceptances cancel, leaving a real conductance. The equivalent resistance is not simply R; it is obtained after adding the two admittances.

Formula / Key Relationship

Yeq = 1/(4+j3)+1/(4−j3)=8/25=0.32 S; Zeq=1/Yeq=3.125 Ω; I=V/Zeq=32 A; PF=cos0°=1.

Step-by-Step Check

Complex-conjugate multiplication gives |4+j3|²=25. Adding admittances cancels ±j3/25 exactly. Numerical current and PF then follow directly, confirming B.

Why the Other Options Are Wrong

Option A is incorrect because it includes incorrect statement(s) 2. Option C is incorrect because it includes incorrect statement(s) 2, 3 and omits correct statement(s) 1, 4. Option D is incorrect because it includes incorrect statement(s) 2, 3.

Answer-Key Verification Note

The uploaded provisional key marks A . After independent technical verification, the defensible answer is B . This discrepancy is stated explicitly rather than silently copying the provisional key.

Exam Shortcut / Approach

For parallel complex branches, convert Z to Y first; it prevents sign and denominator mistakes.

Common Mistake

Directly adding parallel impedances or assuming the equivalent resistance equals the real part of each branch.

Quick Revision

Conjugate Impedances in Parallel is linked with Parallel Complex Impedances, AC Circuits and Basic Electrical Engineering. For parallel complex branches, convert Z to Y first; it prevents sign and denominator mistakes.