Question

A balanced three-phase ∆-connected load is fed from a balanced three-phase circuit. The rms current in the b-phase is 67.8A. Find the rms value (in Ampere) of the line current Iᴀʙ.

Answer 1

The rms value of the line current Iᴀʙ for a balanced three-phase ∆-connected load with a known phase current of 67.8A is 117.4 A.

Step-by-step explanation:

The question concerns a balanced three-phase ∆-connected load where the rms current in one of the phases is known (67.8A for phase 'b'). In a ∆ ('delta') connection, the line current Iᴀʙ is equal to the phase current times the square root of 3 (assuming the load is balanced). Therefore, to find the rms value of the line current Iᴀʙ, you simply perform the following calculation:

• Iᴀʙ = I_phase × √3
• Iᴀʙ = 67.8 A × √3
• Iᴀʙ = 117.4 A

Thus, the rms value of the line current Iᴀʙ is 117.4 A.

Answer 2

The rms value of the line current Iᴀʙ, in a balanced three-phase delta-connected load where the phase current is 67.8A, is approximately 117.5 Ampere.

Step-by-step explanation:

The student is asking about the rms (root mean square) value of the line current in a balanced three-phase delta-connected load. If the rms current in the b-phase is 67.8A, and since it is a balanced delta connection, the line current Iᴀʙ would be equal to the phase current multiplied by the square root of 3 (√3), which is approximately 1.732. Therefore, to find the rms value of the line current Iᴀʙ, we use the formula:

Iᴀʙ = Iₒ-phase × √3

Substituting the given values:

Iᴀʙ = 67.8A × 1.732

Iᴀʙ ≈ 117.5 A

So, the rms value of the line current Iᴀʙ is approximately 117.5 Ampere.