Question

Find resistance in a delta shape terminal.

Answer 1

Concept:
A delta (Δ) network of resistors is a closed-loop configuration where three resistors are connected end-to-end in a triangle-like shape. Each vertex of the triangle represents a terminal. This type of resistor network is common in electrical circuits, especially in balanced 3-phase systems.

The resistance between any two terminals of a delta network depends on the values of the resistors connected between those terminals.

Let the resistors be:
• R_AB between terminals A and B,
• R_BC between terminals B and C,
• R_CA between terminals C and A.

If you want to find the total resistance between any two terminals, say A and B, then the effective resistance is calculated as:

R_{AB (total)} = \(\frac{R_{AB} \cdot (R_{BC} + R_{CA})}{R_{AB} + R_{BC} + R_{CA}}\)

This formula is derived from the concept of converting a delta (Δ) network into an equivalent star (Y) network, which simplifies the computation of equivalent resistances.

Common Misconception:
The expression: \(\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}\) is not applicable directly for a delta connection. That formula is used for parallel resistors. In a delta configuration, resistors are not simply in parallel.

Correct Approach:
Use the formula:
\(R_{AB} = \frac{R_{AB} \cdot (R_{BC} + R_{CA})}{R_{AB} + R_{BC} + R_{CA}}\)
Similar formulas apply for other pairs of terminals.

Conclusion:
In a delta (Δ) configuration, to find resistance between any two terminals, always use the delta resistance formula involving all three resistors. This helps you accurately determine the total resistance seen across any terminal pair in the network.