Three impedances, Z1 =10∠0°Ω, Z2 =20∠30°Ω and Z3 =15∠−60°Ω are connected in star. What is the impedance of Z12 in the equivalent delta network

To find the equivalent delta network impedance Z12, we need to use the formula for converting star to delta impedance. The formula is:

Z12 = (Z1Z2 + Z2Z3 + Z3*Z1) / Z3

Given the values:

Z1 = 10∠0°Ω Z2 = 20∠30°Ω Z3 = 15∠-60°Ω

We can substitute these values into the formula:

Z12 = (10∠0°Ω * 20∠30°Ω + 20∠30°Ω * 15∠-60°Ω + 15∠-60°Ω * 10∠0°Ω) / 15∠-60°Ω

First, we need to multiply the magnitudes and add the angles for each of the terms in the numerator:

= (200∠30°Ω + 300∠-30°Ω + 150∠-60°Ω) / 15∠-60°Ω

Then, we add the terms in the numerator:

= 650∠10°Ω / 15∠-60°Ω

Finally, we divide the magnitudes and subtract the angle in the denominator from the angle in the numerator:

Z12 = 43.33∠70°Ω

So, the impedance of Z12 in the equivalent delta network is 43.33∠70°Ω.