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A delta connection of resistances contains three equal impedances of 60 ohm. The impedance of each arm of the equivalent star connection will be?
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Calculation of Impedance in Star Connection from Delta Connection


Delta Connection


In a delta connection, the resistances are connected in a triangular loop. The impedance of each arm of delta connection is given by the resistance value.

In this case, the delta connection contains three equal impedances of 60 ohm. Therefore, the impedance of each arm of the delta connection is 60 ohm.

Star Connection


To calculate the impedance of each arm in a star connection, we use the following formula:

Zab = Zbc = Zca = Zline/Zphase

where Zline is the line impedance and Zphase is the phase impedance.

In a balanced star connection, the phase impedance is equal to the line impedance divided by the square root of 3.

Therefore, the impedance of each arm in a star connection is given by:

Zab = Zbc = Zca = Zline/(sqrt(3)*Zphase)

Equivalent Star Connection


To find the equivalent star connection, we need to convert the delta connection into a star connection.

The conversion formula for a delta connection to a star connection is:

Zab = Z1*Z2/(Z1+Z2+Z3)
Zbc = Z2*Z3/(Z1+Z2+Z3)
Zca = Z3*Z1/(Z1+Z2+Z3)

In this case, since all the impedances are equal, we can simplify the formula to:

Zab = Zbc = Zca = Z/3

where Z is the impedance of each arm in the delta connection.

Therefore, the impedance of each arm in the equivalent star connection is:

Zab = Zbc = Zca = (60/3)/(sqrt(3)*60) = 0.019+0.011j ohm
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A delta connection of resistances contains three equal impedances of 60 ohm. The impedance of each arm of the equivalent star connection will be?
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