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If each branch of a Delta circuit has impedance √3 Z, then each branch of the equivalent Wye circuit has impedance.
- a)Z/√3
- b)3 Z
- c)3√3 Z
- d)Z/3
Correct answer is option 'A'. Can you explain this answer?
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Understanding Delta to Wye Transformation
In electrical engineering, the transformation between Delta (Δ) and Wye (Y) circuits is essential for simplifying circuit analysis. Here, we’ll discuss the impedance transformation when each branch of a Delta circuit has an impedance of \( \sqrt{3} Z \).
Delta Circuit Impedance
- In a Delta configuration, each branch has an impedance of \( \sqrt{3} Z \).
- This means the three impedances in the Delta circuit are \( Z_1 = Z_2 = Z_3 = \sqrt{3} Z \).
Wye Circuit Impedance Calculation
To find the equivalent Wye impedances (\( Y_1, Y_2, Y_3 \)), we use the formula:
\[
Y_i = \frac{Z_{ij} \cdot Z_{ik}}{Z_{ij} + Z_{ik} + Z_{jk}}
\]
Where \( Z_{ij} \), \( Z_{ik} \), and \( Z_{jk} \) are the impedances of the Delta branches. In our case:
- \( Z_{12} = Z_{13} = Z_{23} = \sqrt{3} Z \).
Using the formula for one branch:
\[
Y_1 = \frac{Z_{12} \cdot Z_{13}}{Z_{12} + Z_{13} + Z_{23}} = \frac{(\sqrt{3} Z)(\sqrt{3} Z)}{(\sqrt{3} Z) + (\sqrt{3} Z) + (\sqrt{3} Z)}
\]
Simplifying:
\[
Y_1 = \frac{3 Z^2}{3 \sqrt{3} Z} = \frac{Z}{\sqrt{3}}
\]
Similarly, we find that \( Y_2 \) and \( Y_3 \) will have the same impedance.
Conclusion
Thus, the impedance of each branch in the equivalent Wye circuit is:
\[
\boxed{\frac{Z}{\sqrt{3}}}
\]
This confirms that the correct answer is option 'A', \( \frac{Z}{\sqrt{3}} \).
In electrical engineering, the transformation between Delta (Δ) and Wye (Y) circuits is essential for simplifying circuit analysis. Here, we’ll discuss the impedance transformation when each branch of a Delta circuit has an impedance of \( \sqrt{3} Z \).
Delta Circuit Impedance
- In a Delta configuration, each branch has an impedance of \( \sqrt{3} Z \).
- This means the three impedances in the Delta circuit are \( Z_1 = Z_2 = Z_3 = \sqrt{3} Z \).
Wye Circuit Impedance Calculation
To find the equivalent Wye impedances (\( Y_1, Y_2, Y_3 \)), we use the formula:
\[
Y_i = \frac{Z_{ij} \cdot Z_{ik}}{Z_{ij} + Z_{ik} + Z_{jk}}
\]
Where \( Z_{ij} \), \( Z_{ik} \), and \( Z_{jk} \) are the impedances of the Delta branches. In our case:
- \( Z_{12} = Z_{13} = Z_{23} = \sqrt{3} Z \).
Using the formula for one branch:
\[
Y_1 = \frac{Z_{12} \cdot Z_{13}}{Z_{12} + Z_{13} + Z_{23}} = \frac{(\sqrt{3} Z)(\sqrt{3} Z)}{(\sqrt{3} Z) + (\sqrt{3} Z) + (\sqrt{3} Z)}
\]
Simplifying:
\[
Y_1 = \frac{3 Z^2}{3 \sqrt{3} Z} = \frac{Z}{\sqrt{3}}
\]
Similarly, we find that \( Y_2 \) and \( Y_3 \) will have the same impedance.
Conclusion
Thus, the impedance of each branch in the equivalent Wye circuit is:
\[
\boxed{\frac{Z}{\sqrt{3}}}
\]
This confirms that the correct answer is option 'A', \( \frac{Z}{\sqrt{3}} \).
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If each branch of a Delta circuit has impedance√3 Z, then each branch of the equivalent Wye circuit has impedance.a)Z/√3b)3 Zc)3√3 Zd)Z/3Correct answer is option 'A'. Can you explain this answer?
Question Description
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