Question

A star circuit has element of resistance r/2. The equivalent delta elements will be

Answer 1

See the Star network and delta network.

The value of the element resistor on any one side of the delta network is the sum of all the two-product combinations of element resistors in the star network divide by the star resistor located “directly opposite” the delta element resistor being found.

For example, element A resistance in delta is given as:

A = (PQ+QR+PR)/R.

Here each P, Q and R are r/2.

Hence you get A = (3r*r/4) * (r/2) = 3r/2

B =  (PQ+QR+PR) / Q = 3r/2

C = (PQ+QR+PR) / P = 3r/2

Answer 2

Answer:

The equivalent delta elements are 3r/2.

Relations to be noted:

star to delta conversion: Delta element resistance = (sum of the product of two resistance at a time) / resistance of opposite branch

Explanation:

Given that the resistance of the star element = r/2

Now the resistance of the element of the delta = $\frac{(\frac{r^{2} }{4} + \frac{r^{2} }{4} + \frac{r^{2} }{4} )}{\frac{r}{2} } = \frac{3r}{2}$.