# If the impedance of each phase of a balanced star-connected load is (3 + 2j) Ω, what will be the impedance of the equivalent delta-connected load?

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DSSSB JE EE 2019 Official Paper (Held on 25 Oct 2019)
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1. (3 + j2) Ω
2. (9 + j6) Ω
3. (3 + j6) Ω
4. (2 + j3) Ω

Option 2 : (9 + j6) Ω

## Detailed Solution

Concept: 1) Delta to Star conversion:

$${R_A} = \dfrac{{{R_{AB}} \times {R_{AC}}}}{{{R_{AB}} + {R_{AC}} + {R_{BC}}}}$$

$${R_B} = \dfrac{{{R_{AB}} \times {R_{BC}}}}{{{R_{AB}} + {R_{AC}} + {R_{BC}}}}$$

$${R_C} = \dfrac{{{R_{BC}} \times {R_{AC}}}}{{{R_{AB}} + {R_{AC}} + {R_{BC}}}}$$

2) Star to Delta conversion:

$${R_{AB}} = \dfrac{{({R_A} \times {R_C}) + ({R_A} \times {R_B})+({R_B} \times {R_C})}}{{{R_C}}}$$

$${R_{AC}} = \dfrac{{({R_A} \times {R_C}) + ({R_A} \times {R_B})+({R_B} \times {R_C})}}{{{R_B}}}$$

$${R_{BC}} = \dfrac{{({R_A} \times {R_C}) + ({R_A} \times {R_B})+({R_B} \times {R_C})}}{{{R_A}}}$$

This concept is valid not only for Resistances but also for any

impedance.

If all the branch Impedances of the star network are equal to Z,

then each branch in its equivalent delta network is equal to 3 Z.

Application:

Given: Zan = Zbn = Zcn = (3 + j 2) Ω

According to the question, by converting the given Star to Delta, we get

$$Z_{AC}=Z_{AB}=Z_{BC}=3Z_{an}$$

= 3 (3 + j 2) Ω

= (9 + j 6) Ω
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