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

Z12 = (Z1*Z2 + Z2*Z3 + 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.

Question

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

Z12 = (Z1*Z2 + Z2*Z3 + 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.

Knowee AI · Accepted Answer