Question

If three equal resistances of \(12\Omega\) are connected in Delta, then each resistance of the equivalent Star is

• A. \(4\Omega\)
• B. \(6\Omega\)
• C. \(12\Omega\)
• D. \(36\Omega\)

Hint:

Delta to Star (balanced): \(R_Y = R_\Delta / 3\).
Star to Delta (balanced): \(R_\Delta = 3 R_Y\).

Answer 1

The Correct Option is A

For a balanced Delta (\(\Delta\)) connection with three equal resistances \(R_\Delta\), the equivalent Star (Y) connection will also have three equal resistances \(R_Y\). The formula for conversion is: \[ R_Y = \frac{R_\Delta}{3} \] Given \(R_\Delta = 12\Omega\). \[ R_Y = \frac{12\Omega}{3} = 4\Omega \] Each resistance of the equivalent Star is \(4\Omega\). \[ \boxed{4\Omega} \]