In a three-phase system for delta connection, the phasor relation between line current I_L and the corresponding phase current I_ph is:

Explanation:

In a three-phase system, the delta connection is one of the two standard methods of connecting the windings of a three-phase system, the other being the star (or wye) connection. The delta connection is characterized by the end of each winding being connected to the start of the next, forming a closed loop or triangle. This configuration has several implications for the relationship between the phase currents and the line currents in the system.

Delta Connection:

In a delta connection, the three windings of the electrical system are connected end-to-end to form a closed loop. Each corner of the delta is connected to a line conductor. The voltage across each winding is the same as the line voltage, but the currents in the windings (phase currents) and the currents in the line conductors (line currents) have a specific relationship that is different from the star connection.

Phasor Relation between Line Current and Phase Current:

In a delta connection, the line current (IL) is related to the phase current (Iph) by both magnitude and phase angle. The key points to understand are:

• The line current is the vector sum of the currents in the two windings that meet at the corresponding line connection point.
• The magnitude of the line current is √3 times the magnitude of the phase current.
• The line current lags the phase current by 30 degrees.

To illustrate, consider the following:

• If Iph is the current in one phase winding, the line current IL can be found by summing the currents from the two windings that share a common point at the line connection. This involves vector addition, taking into account the phase angles.
• Mathematically, this can be expressed as IL = √3 * Iph, with a phase difference where IL lags Iph by 30 degrees.

Correct Option Analysis:

The correct option is:

Option 2: IL lags Iph by 30 degrees.

This option correctly describes the phasor relationship between the line current and the phase current in a delta connection. The line current is not only √3 times the magnitude of the phase current but also lags the phase current by 30 degrees.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: IL leads Iph by 30 degrees.

This option is incorrect because, in a delta connection, the line current actually lags the phase current by 30 degrees, not leads.

Option 3: IL is in phase with Iph.

This option is incorrect as well because the line current is not in phase with the phase current. There is a 30-degree phase shift where the line current lags the phase current.

Option 4: IL leads Iph by 90 degrees.

This option is incorrect because a 90-degree phase shift is not characteristic of the relationship between line current and phase current in a delta connection.

Conclusion:

Understanding the phasor relationships in a three-phase delta connection is crucial for analyzing and designing electrical systems. The correct relationship is that the line current lags the phase current by 30 degrees and has a magnitude of √3 times the phase current. This fundamental knowledge helps in ensuring proper system operation and troubleshooting in practical applications.