Question

Three resistance of 20 ohm each are. Connected in star . Find the equivalent delta resistance

Answer 1

Explanation:

R=( r*r+ r*r+ r*r) /r = 3r^2 / r = 3r

3r =3*20 =60

Answer 2

The equivalent delta resistance of three 20 ohm resistors connected in the star is 80 ohm.

Given,

Three resistance of 20 ohms each are connected in a star shape.

To find,

The equivalent delta resistance.

Solution,

To find the equivalent delta resistance (Rᵟ), we can use the following formula:

Rᵟ = (RaRb + RbRc + Rc*Ra)/Rs

where Ra, Rb, and Rc are the resistances of the three arms of the delta connection and Rs is the resistance between any two terminals.

To convert the star connection to delta, we can use the following equations:

R1 = RbRc / (Rb+Rc+Ra)

R2 = RaRc / (Ra+Rc+Rb)

R3 = Ra*Rb / (Ra+Rb+Rc)

Substituting the given values of Ra, Rb, and Rc as 20 ohms each, we get:

R1 = (20 * 20) / (20 + 20 + 20) = 6.67 ohm

R2 = (20 * 20) / (20 + 20 + 20) = 6.67 ohm

R3 = (20 * 20) / (20 + 20 + 20) = 6.67 ohm

Now, to find Rs, we can connect a resistance meter between any two terminals of the star connection. Let's assume we connect the meter between terminals A and B and measure the resistance as RAB.

In this case, RAB can be found using the following formula:

RAB = R1 + R2 + ((R1*R2)/(R1+R2+R3))

Substituting the values of R1, R2, and R3, we may get:

RAB = 6.67 + 6.67 + ((6.67*6.67)/(6.67+6.67+6.67)) = 13.33 ohm

Now, we can use the formula for Rᵟ to get the equivalent delta resistance:

Rᵟ = (RaRb + RbRc + Rc*Ra)/Rs

Substituting the values of Ra, Rb, Rc, and Rs, we get:

Rᵟ = (2020 + 2020 + 20*20)/13.33 = 80 ohm

The equivalent delta resistance is 80 ohm.

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