Basic Electrical Engineering (3110005)

Winter-2019

Question-1c

BE | Semester-1 Winter-2019 | 11-01-2020

Q1) (c)

Derive an expression for equivalent resistances of a star connected network to transform into a Delta connected network.

As per Delta to Star transformation, we have

R_{1} = \frac{R_{12} \times R_{31}}{R_{12} + R_{23} + R_{31}} . . . . . . . . . . . . . . . . . . . . . (1)

R_{2} = \frac{R_{23} \times R_{12}}{R_{12} + R_{23} + R_{31}} . . . . . . . . . . . . . . . . . . . . . (2)

R_{3} = \frac{R_{31} \times R_{23}}{R_{12} + R_{23} + R_{31}} . . . . . . . . . . . . . . . . . . . . . (3)

Dividing equation (1) by equation (2),

\frac{R_{1}}{R_{2}} = \frac{R_{31}}{R_{23}}

\Rightarrow R_{31} = \frac{R_{1} \times R_{23}}{R_{2}} . . . . . . . . . . . . . . . . . . . . . (4)

Similarly,

\frac{R_{1}}{R_{3}} = \frac{R_{12}}{R_{23}}

\Rightarrow R_{12} = \frac{R_{1} \times R_{23}}{R_{3}} . . . . . . . . . . . . . . . . . . . . . (5)

Substituting the value of

R_{31}

and

R_{12}

in equation ( 1 ) and reshuffling the quantities,

\Rightarrow R_{23} = R_{2} + R_{3} + \frac{R_{2} \times R_{3}}{R_{1}} . . . . . . . . . . . . . . . . . . . . . (6)

Similarly,

\Rightarrow R_{31} = R_{3} + R_{1} + \frac{R_{3} \times R_{1}}{R_{2}} . . . . . . . . . . . . . . . . . . . . . (7)

\Rightarrow R_{12} = R_{1} + R_{2} + \frac{R_{1} \times R_{2}}{R_{3}} . . . . . . . . . . . . . . . . . . . . . (8)

Hence,

Resistance of any arm of Delta = Sum of Star resistances connected across that arm + Product of the same two resistances divided by the third resistance

Basic Electrical Engineering (3110005)

Q1) (c)

Derive an expression for equivalent resistances of a star connected network to transform into a Delta connected network.

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