  # The power taken by a 3-ϕ load is given by the expression?

By BYJU'S Exam Prep

Updated on: October 17th, 2023 (A) 3 VLIL cos ϕ

(B) √3 VLIL cos ϕ

(C) 3 VLIL sin ϕ

(D) √3 VLIL sin ϕ

The power taken by a 3-ϕ load is given by the expression √3 VLIL cos ϕ. A single phase system’s power, the power triangle, is depicted as follows: P = Active power (or) Real power in W = V I cos ϕ

Q = Reactive power in VAR = V I sin ϕ

S = Apparent power in VA = V I

S = P + jQ

S = √P2 + Q2

ϕ is the phase difference between the voltage and current.

The power in a balanced three-phase system (for both star and delta connected) is,

Active power (P) = √3 VL IL cos ϕ

Reactive power (Q) = √3 VL IL sin ϕ

Apparent power (S) = √3 VL IL

In a three-phase load, three different impedances are connected together in a star or delta fashion.

In a star-connected three-phase system,

V = √3 × Vph And IL = Iph

Iph = VL/√3 z

In a delta-connected three-phase system,

VL = Vph

IL = √3 × Iph

Iph = VL/z

Where,

VL is line voltage

Vph is phase voltage

IL is line current

Iph is the phase current

Summary:

## The power taken by a 3-ϕ load is given by the expression? (A) 3 VLIL cos ϕ (B) √3 VLIL cos ϕ (C) 3 VLIL sin ϕ (D) √3 VLIL sin ϕ

The power taken by a 3-ϕ load is given by the expression √3 VLIL cos ϕ, so option A is correct and rest of the options are wrong here. These questions are usually asked in the competitive exams or entrance exams of reputed institutions.

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