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If a 8/9ohm, 4/3ohm and 2/3ohm resistor is connected in star, find its delta equivalent.
- a)4ohm, 3ohm, 2ohm
- b)1ohm, 3ohm, 2ohm
- c)4ohm, 1ohm, 2ohm
- d)4ohm, 3ohm, 1ohm
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If a 8/9ohm, 4/3ohm and 2/3ohm resistor is connected in star, find its...
Using the formula for star to delta conversion:
R1=8/9+4/3+(8/9)*(4/3)/(2/3)
R2=8/9+2/3+(8/9)*(2/3)/(4/3)
R3=2/3+4/3+(2/3)*(4/3)/(8/9).
R1=8/9+4/3+(8/9)*(4/3)/(2/3)
R2=8/9+2/3+(8/9)*(2/3)/(4/3)
R3=2/3+4/3+(2/3)*(4/3)/(8/9).
Most Upvoted Answer
If a 8/9ohm, 4/3ohm and 2/3ohm resistor is connected in star, find its...
Given:
Resistor 1 (R1) = 8/9 ohm
Resistor 2 (R2) = 4/3 ohm
Resistor 3 (R3) = 2/3 ohm
To find the delta equivalent of the star-connected resistors, we need to calculate the equivalent resistance for each branch of the delta network.
1. Calculate the equivalent resistance for branch a:
The equivalent resistance for branch a can be found by using the formula:
1/Ra = 1/R1 + 1/R2
Substituting the given values:
1/Ra = 1/(8/9) + 1/(4/3)
1/Ra = 9/8 + 3/4
1/Ra = (9 + 6)/8
1/Ra = 15/8
Ra = 8/15 ohm
2. Calculate the equivalent resistance for branch b:
The equivalent resistance for branch b can be found by using the formula:
1/Rb = 1/R2 + 1/R3
Substituting the given values:
1/Rb = 1/(4/3) + 1/(2/3)
1/Rb = 3/4 + 3/2
1/Rb = (3 + 6)/4
1/Rb = 9/4
Rb = 4/9 ohm
3. Calculate the equivalent resistance for branch c:
The equivalent resistance for branch c can be found by using the formula:
1/Rc = 1/R1 + 1/R3
Substituting the given values:
1/Rc = 1/(8/9) + 1/(2/3)
1/Rc = 9/8 + 3/2
1/Rc = (9 + 12)/8
1/Rc = 21/8
Rc = 8/21 ohm
4. Now, we have the equivalent resistances for each branch of the delta network:
Ra = 8/15 ohm
Rb = 4/9 ohm
Rc = 8/21 ohm
Therefore, the delta equivalent of the given star-connected resistors is:
a) 8/15 ohm, 4/9 ohm, 8/21 ohm
The correct answer is option 'A': 8/15 ohm, 4/9 ohm, 8/21 ohm.
Resistor 1 (R1) = 8/9 ohm
Resistor 2 (R2) = 4/3 ohm
Resistor 3 (R3) = 2/3 ohm
To find the delta equivalent of the star-connected resistors, we need to calculate the equivalent resistance for each branch of the delta network.
1. Calculate the equivalent resistance for branch a:
The equivalent resistance for branch a can be found by using the formula:
1/Ra = 1/R1 + 1/R2
Substituting the given values:
1/Ra = 1/(8/9) + 1/(4/3)
1/Ra = 9/8 + 3/4
1/Ra = (9 + 6)/8
1/Ra = 15/8
Ra = 8/15 ohm
2. Calculate the equivalent resistance for branch b:
The equivalent resistance for branch b can be found by using the formula:
1/Rb = 1/R2 + 1/R3
Substituting the given values:
1/Rb = 1/(4/3) + 1/(2/3)
1/Rb = 3/4 + 3/2
1/Rb = (3 + 6)/4
1/Rb = 9/4
Rb = 4/9 ohm
3. Calculate the equivalent resistance for branch c:
The equivalent resistance for branch c can be found by using the formula:
1/Rc = 1/R1 + 1/R3
Substituting the given values:
1/Rc = 1/(8/9) + 1/(2/3)
1/Rc = 9/8 + 3/2
1/Rc = (9 + 12)/8
1/Rc = 21/8
Rc = 8/21 ohm
4. Now, we have the equivalent resistances for each branch of the delta network:
Ra = 8/15 ohm
Rb = 4/9 ohm
Rc = 8/21 ohm
Therefore, the delta equivalent of the given star-connected resistors is:
a) 8/15 ohm, 4/9 ohm, 8/21 ohm
The correct answer is option 'A': 8/15 ohm, 4/9 ohm, 8/21 ohm.
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