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Three 3μ F capacitors are in series. A 6 capacitor is in parallel with this series arrangement. The equivalent capacitance of this combination is-
- a)7μ F
- b)15μ F
- c)3.6μ F
- d)1μ F
Correct answer is option 'A'. Can you explain this answer?
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Three 3μ F capacitors are in series. A 6 capacitor is in parallel wit...
Cab = (1e)μ F = 7μ F
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Three 3μ F capacitors are in series. A 6 capacitor is in parallel wit...
To find the equivalent capacitance of the given combination, we need to apply the rules of series and parallel combination of capacitors.
Given:
Three 3μF capacitors are in series.
A 6μF capacitor is in parallel with this series arrangement.
Let's solve this step by step.
Step 1: Capacitors in Series
When capacitors are connected in series, the reciprocal of the equivalent capacitance is equal to the sum of the reciprocals of the individual capacitances.
In this case, the three 3μF capacitors are in series. So, the equivalent capacitance of these three capacitors in series can be found as:
1/Ceq = 1/C1 + 1/C2 + 1/C3
Substituting the given values:
1/Ceq = 1/3μF + 1/3μF + 1/3μF
1/Ceq = 3/3μF
1/Ceq = 1μF
Therefore, the equivalent capacitance of the three 3μF capacitors in series is 1μF.
Step 2: Capacitor in Parallel
When capacitors are connected in parallel, the equivalent capacitance is the sum of the individual capacitances.
In this case, the 6μF capacitor is in parallel with the series arrangement of capacitors. So, the equivalent capacitance of the combination can be found as:
Ceq = Cseries + Cparallel
Ceq = 1μF + 6μF
Ceq = 7μF
Therefore, the equivalent capacitance of the given combination is 7μF.
Hence, the correct answer is option A) 7μF.
Given:
Three 3μF capacitors are in series.
A 6μF capacitor is in parallel with this series arrangement.
Let's solve this step by step.
Step 1: Capacitors in Series
When capacitors are connected in series, the reciprocal of the equivalent capacitance is equal to the sum of the reciprocals of the individual capacitances.
In this case, the three 3μF capacitors are in series. So, the equivalent capacitance of these three capacitors in series can be found as:
1/Ceq = 1/C1 + 1/C2 + 1/C3
Substituting the given values:
1/Ceq = 1/3μF + 1/3μF + 1/3μF
1/Ceq = 3/3μF
1/Ceq = 1μF
Therefore, the equivalent capacitance of the three 3μF capacitors in series is 1μF.
Step 2: Capacitor in Parallel
When capacitors are connected in parallel, the equivalent capacitance is the sum of the individual capacitances.
In this case, the 6μF capacitor is in parallel with the series arrangement of capacitors. So, the equivalent capacitance of the combination can be found as:
Ceq = Cseries + Cparallel
Ceq = 1μF + 6μF
Ceq = 7μF
Therefore, the equivalent capacitance of the given combination is 7μF.
Hence, the correct answer is option A) 7μF.
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Three 3μ F capacitors are in series. A 6 capacitor is in parallel with this series arrangement. The equivalent capacitance of this combination is-a)7μ Fb)15μ Fc)3.6μ Fd)1μ FCorrect answer is option 'A'. Can you explain this answer?
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