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Three capacitances, each of C/3 Farads are connected in delta. Their equivalent star value for each capacitance is
- a)3C
- b)C
- c)2/3C
- d)2C
Correct answer is option 'B'. Can you explain this answer?
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Equivalent Star Value of Capacitances Connected in Delta
When three capacitances, each of C/3 Farads, are connected in delta, we need to find their equivalent star value. The equivalent capacitance in star (C_s) can be calculated using the formula:
C_s = C_d/(C_a + C_b + C_c)
where C_d is the delta capacitance and C_a, C_b, and C_c are the individual capacitances connected in delta.
Step-by-Step Solution:
Step 1: Given that each capacitance is C/3 Farads.
Step 2: To find the delta capacitance (C_d), we need to calculate the sum of all three capacitances connected in delta.
C_d = C_a + C_b + C_c
Substituting the given values, we have:
C_d = (C/3) + (C/3) + (C/3)
C_d = C
Step 3: Now, we can substitute the values of C_d, C_a, C_b, and C_c in the formula for the equivalent star capacitance (C_s).
C_s = C_d/(C_a + C_b + C_c)
C_s = C/(C/3 + C/3 + C/3)
C_s = C/(3C/3)
C_s = C/C
C_s = 1
Step 4: The equivalent star value of the three capacitances connected in delta is 1 Farad.
Conclusion:
The correct answer is option 'B' - C. The equivalent star value for each capacitance connected in delta is C.
When three capacitances, each of C/3 Farads, are connected in delta, we need to find their equivalent star value. The equivalent capacitance in star (C_s) can be calculated using the formula:
C_s = C_d/(C_a + C_b + C_c)
where C_d is the delta capacitance and C_a, C_b, and C_c are the individual capacitances connected in delta.
Step-by-Step Solution:
Step 1: Given that each capacitance is C/3 Farads.
Step 2: To find the delta capacitance (C_d), we need to calculate the sum of all three capacitances connected in delta.
C_d = C_a + C_b + C_c
Substituting the given values, we have:
C_d = (C/3) + (C/3) + (C/3)
C_d = C
Step 3: Now, we can substitute the values of C_d, C_a, C_b, and C_c in the formula for the equivalent star capacitance (C_s).
C_s = C_d/(C_a + C_b + C_c)
C_s = C/(C/3 + C/3 + C/3)
C_s = C/(3C/3)
C_s = C/C
C_s = 1
Step 4: The equivalent star value of the three capacitances connected in delta is 1 Farad.
Conclusion:
The correct answer is option 'B' - C. The equivalent star value for each capacitance connected in delta is C.
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Three capacitances, each of C/3 Farads are connected in delta. Their equivalent star value for each capacitance isa)3Cb)Cc)2/3Cd)2CCorrect answer is option 'B'. Can you explain this answer?
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