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There are three capacitors with equal capacitance. In series combination, they have a net capacitance of C1 and in parallel combination, a net capacitance of C2.What will be the value of C1 C2?
- a)1:9
- b)3:2
- c)2:3
- d)9:1
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
There are three capacitors with equal capacitance. In series combinati...
For series combination,
1/C1=(1/C)+(1/C)+(1/C) [ Since all capacitors have equal capacitances]=3/C Or
C1=C/3−−−(i)
For parallel combination,
C2=C+C+C=3C−−−(ii)
Now,C1/C2=(C/3)/3C=(C/3)×(1/3C)=1/9
1/C1=(1/C)+(1/C)+(1/C) [ Since all capacitors have equal capacitances]=3/C Or
C1=C/3−−−(i)
For parallel combination,
C2=C+C+C=3C−−−(ii)
Now,C1/C2=(C/3)/3C=(C/3)×(1/3C)=1/9
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There are three capacitors with equal capacitance. In series combinati...
Solution:
Given: Three capacitors of equal capacitance; in series combination, they have a net capacitance of C1, and in parallel combination, they have a net capacitance of C2.
Let the capacitance of each capacitor be C.
In series combination, the net capacitance is given by:
1/Ceq = 1/C + 1/C + 1/C
1/Ceq = 3/C
Ceq = C/3
Therefore, C1 = C/3
In parallel combination, the net capacitance is given by:
Ceq = C + C + C
Ceq = 3C
Therefore, C2 = 3C
We need to find the value of C1C2.
C1C2 = (C/3) × 3C
C1C2 = C²
Hence, the ratio of C1 to C2 is 1:9.
Therefore, the correct answer is option A.
Summary:
Three capacitors of equal capacitance are given. In series combination, they have a net capacitance of C1, and in parallel combination, they have a net capacitance of C2. We need to find the value of C1C2. Using the formulas for the net capacitance in series and parallel combinations, we can express C1 and C2 in terms of C. Substituting these values, we get C1C2 = C², which gives the ratio of C1 to C2 as 1:9. Hence, the correct answer is option A.
Given: Three capacitors of equal capacitance; in series combination, they have a net capacitance of C1, and in parallel combination, they have a net capacitance of C2.
Let the capacitance of each capacitor be C.
In series combination, the net capacitance is given by:
1/Ceq = 1/C + 1/C + 1/C
1/Ceq = 3/C
Ceq = C/3
Therefore, C1 = C/3
In parallel combination, the net capacitance is given by:
Ceq = C + C + C
Ceq = 3C
Therefore, C2 = 3C
We need to find the value of C1C2.
C1C2 = (C/3) × 3C
C1C2 = C²
Hence, the ratio of C1 to C2 is 1:9.
Therefore, the correct answer is option A.
Summary:
Three capacitors of equal capacitance are given. In series combination, they have a net capacitance of C1, and in parallel combination, they have a net capacitance of C2. We need to find the value of C1C2. Using the formulas for the net capacitance in series and parallel combinations, we can express C1 and C2 in terms of C. Substituting these values, we get C1C2 = C², which gives the ratio of C1 to C2 as 1:9. Hence, the correct answer is option A.
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There are three capacitors with equal capacitance. In series combination, they have a net capacitance of C1and in parallel combination, a net capacitance of C2.What will be the value of C1C2?a)1:9b)3:2c)2:3d)9:1Correct answer is option 'A'. Can you explain this answer?
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