Question

If each branch of a Delta circuit has impedance $\sqrt{3}\,Z$, then each branch of the equivalent Wye circuit has impedance

• A. $\dfrac{Z}{\sqrt{3}}$
• B. $3Z$
• C. $3\sqrt{3}\,Z$
• D. $\dfrac{Z}{3}$

Hint:

For balanced networks, remember: $\; Z_Y = \dfrac{Z_{\Delta}}{3}$. This formula directly helps in quick Delta–Wye conversions.

Answer 1

The Correct Option is A

Step 1: Recall Delta to Wye conversion formula.
In a Delta ($\Delta$) connected circuit, if each branch has impedance $Z_{\Delta}$, then the equivalent Wye (Y) impedance $Z_Y$ is given by:
\[ Z_Y = \frac{Z_{\Delta}}{3} \]
Step 2: Substitute the given value.
It is given that each branch of the Delta circuit has impedance:
\[ Z_{\Delta} = \sqrt{3}\,Z \]
Substituting into the formula:
\[ Z_Y = \frac{\sqrt{3}\,Z}{3} \]
Step 3: Simplify the expression.
\[ Z_Y = \frac{Z}{\sqrt{3}} \]
Step 4: Match with the given options.
The obtained result matches option (A).
Step 5: Final conclusion.
Hence, each branch of the equivalent Wye circuit has impedance $\dfrac{Z}{\sqrt{3}}$.