Two resistors of 6 Ω and 3 Ω are connected in parallel across 12 V supply. Then1.Equivalent resistance is 2 Ω.2.Total current is 6 A.3.Current through 3 Ω resistor is 4 A.4.Power consumed is 72 W.Which of the above statements is/are correct?

Correct Answer: D - All of the above

Quick Concept Explanation

Equivalent resistance is found from reciprocal addition, total current is the sum of branch currents, and total real power is the sum of branch powers. For 6 Ω || 3 Ω, Req=(6×3)/(6+3)=2 Ω. Total current=12/2=6 A. Key relation: 1/R_eq=Σ(1/R_i); I_i=V/R_i; P_total=V I_total.

Exam focus: Solve branch currents first when the same supply voltage appears across every resistor. Common trap: Adding parallel resistances directly is incorrect.

Statement-wise Verification

• Statement 1 - Correct.
  Equivalent resistance is 2 Ω.
  Equivalent resistance is found from reciprocal addition, total current is the sum of branch currents, and total real power is the sum of branch powers.
• Statement 2 - Correct.
  Total current is 6 A.
  Total current=12/2=6 A.
• Statement 3 - Correct.
  Current through 3 Ω resistor is 4 A.
  The 3 Ω branch current=12/3=4 A.
• Statement 4 - Correct.
  Power consumed is 72 W.
  Total power=12×6=72 W.

Core Concept

Parallel branches share the same voltage. Equivalent resistance is found from reciprocal addition, total current is the sum of branch currents, and total real power is the sum of branch powers.

Formula / Key Relationship

1/R_eq=Σ(1/R_i); I_i=V/R_i; P_total=V I_total.

Step-by-Step Check

For 6 Ω || 3 Ω, Req=(6×3)/(6+3)=2 Ω. Total current=12/2=6 A. The 3 Ω branch current=12/3=4 A. Total power=12×6=72 W.

Why the Other Options Are Wrong

Option A is incorrect because it omits correct statement(s) 3, 4. Option B is incorrect because it omits correct statement(s) 4. Option C is incorrect because it omits correct statement(s) 1, 3.

Exam Shortcut / Approach

Solve branch currents first when the same supply voltage appears across every resistor.

Common Mistake

Adding parallel resistances directly is incorrect.

Quick Revision

Parallel Resistor Current and Power is linked with Parallel Resistance, DC Circuits and Basic Electrical Engineering. Solve branch currents first when the same supply voltage appears across every resistor.