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If a 1ohm 2ohm and 32/3ohm resistor is connected in star, find the equivalent delta connection.
- a)1ohm, 3ohm, 2ohm
- b)4ohm, 3ohm, 5ohm
- c)4ohm, 5ohm, 2ohm
- d)5ohm, 3ohm, 2ohm
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If a 1ohm 2ohm and 32/3ohm resistor is connected in star, find the equ...
Using the formula for delta to star conversion:
R1=1+2+1*2/(32/3)
R2=1+32/3+1*32/3/2
R3=2+32/3+2*32/3/1.
R1=1+2+1*2/(32/3)
R2=1+32/3+1*32/3/2
R3=2+32/3+2*32/3/1.
This question is part of UPSC exam. View all Electrical Engineering (EE) courses
Most Upvoted Answer
If a 1ohm 2ohm and 32/3ohm resistor is connected in star, find the equ...
To find the equivalent delta connection for the given resistors in a star connection, we can use the following formula:
R1 = (Rab * Rbc + Rbc * Rca + Rca * Rab) / (Rab + Rbc + Rca)
Where R1, R2, and R3 are the resistances of the delta-connected resistors, and Rab, Rbc, and Rca are the resistances of the star-connected resistors.
Let's calculate the equivalent delta connection step by step:
1. Identify the resistances in the star connection:
- R1 = 1 ohm
- R2 = 2 ohms
- R3 = 32/3 ohms
2. Apply the formula to find the equivalent delta-connected resistances:
R1 = (Rab * Rbc + Rbc * Rca + Rca * Rab) / (Rab + Rbc + Rca)
Substitute the given resistor values:
1 = (Rab * Rbc + Rbc * Rca + Rca * Rab) / (Rab + Rbc + Rca)
We need to solve this equation to find the values of Rab, Rbc, and Rca.
3. Simplify the equation:
Multiply both sides of the equation by (Rab + Rbc + Rca) to eliminate the denominator:
(Rab + Rbc + Rca) = Rab * Rbc + Rbc * Rca + Rca * Rab
Expand the equation:
Rab + Rbc + Rca = Rab * Rbc + Rbc * Rca + Rca * Rab
Rearrange the terms:
Rab + Rbc + Rca - Rab * Rbc - Rbc * Rca - Rca * Rab = 0
Factor out common factors:
Rab(1 - Rbc) + Rbc(1 - Rca) + Rca(1 - Rab) = 0
4. Solve for the values of Rab, Rbc, and Rca:
To satisfy the equation, we can set Rab = 1, Rbc = 3, and Rca = 2.
Therefore, the equivalent delta-connected resistances are:
R1 = 1 ohm
R2 = 3 ohms
R3 = 2 ohms
Hence, option A (1 ohm, 3 ohm, 2 ohm) is the correct answer.
R1 = (Rab * Rbc + Rbc * Rca + Rca * Rab) / (Rab + Rbc + Rca)
Where R1, R2, and R3 are the resistances of the delta-connected resistors, and Rab, Rbc, and Rca are the resistances of the star-connected resistors.
Let's calculate the equivalent delta connection step by step:
1. Identify the resistances in the star connection:
- R1 = 1 ohm
- R2 = 2 ohms
- R3 = 32/3 ohms
2. Apply the formula to find the equivalent delta-connected resistances:
R1 = (Rab * Rbc + Rbc * Rca + Rca * Rab) / (Rab + Rbc + Rca)
Substitute the given resistor values:
1 = (Rab * Rbc + Rbc * Rca + Rca * Rab) / (Rab + Rbc + Rca)
We need to solve this equation to find the values of Rab, Rbc, and Rca.
3. Simplify the equation:
Multiply both sides of the equation by (Rab + Rbc + Rca) to eliminate the denominator:
(Rab + Rbc + Rca) = Rab * Rbc + Rbc * Rca + Rca * Rab
Expand the equation:
Rab + Rbc + Rca = Rab * Rbc + Rbc * Rca + Rca * Rab
Rearrange the terms:
Rab + Rbc + Rca - Rab * Rbc - Rbc * Rca - Rca * Rab = 0
Factor out common factors:
Rab(1 - Rbc) + Rbc(1 - Rca) + Rca(1 - Rab) = 0
4. Solve for the values of Rab, Rbc, and Rca:
To satisfy the equation, we can set Rab = 1, Rbc = 3, and Rca = 2.
Therefore, the equivalent delta-connected resistances are:
R1 = 1 ohm
R2 = 3 ohms
R3 = 2 ohms
Hence, option A (1 ohm, 3 ohm, 2 ohm) is the correct answer.
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