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Two capacitor in series with 1000v of store of energy of 0.6J while the same two capacitor in parallel across the same sorce of 2.5 J .calculate the capacitance of each capacitor?
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Calculating Capacitance of Two Capacitors in Series and Parallel


Introduction

When capacitors are connected in series or parallel, their combined capacitance changes. In this problem, we are given two capacitors that are connected in series and parallel with a voltage source, and we are asked to calculate their capacitance.

Calculating Capacitance in Series

When capacitors are connected in series, their effective capacitance decreases. The formula for calculating the effective capacitance of capacitors in series is:

1/Ceq = 1/C1 + 1/C2 + ...

Where Ceq is the effective capacitance of the capacitors in series, and C1 and C2 are the capacitances of the individual capacitors.

In this problem, we are given that the two capacitors in series have a store of energy of 0.6J when connected to a 1000V source. We can use this information to calculate the effective capacitance of the capacitors in series.

E = 1/2 * Ceq * V^2

0.6J = 1/2 * Ceq * (1000V)^2

Ceq = 1.2 * 10^-6 F

Therefore, the effective capacitance of the capacitors in series is 1.2 microfarads.

Calculating Capacitance in Parallel

When capacitors are connected in parallel, their effective capacitance increases. The formula for calculating the effective capacitance of capacitors in parallel is:

Ceq = C1 + C2 + ...

Where Ceq is the effective capacitance of the capacitors in parallel, and C1 and C2 are the capacitances of the individual capacitors.

In this problem, we are given that the two capacitors in parallel have a store of energy of 2.5J when connected to the same 1000V source. We can use this information to calculate the effective capacitance of the capacitors in parallel.

E = 1/2 * Ceq * V^2

2.5J = 1/2 * (C1 + C2) * (1000V)^2

C1 + C2 = 5 * 10^-6 F

We also know from the previous calculation that the effective capacitance of the capacitors in series is 1.2 microfarads. We can use this information to calculate the individual capacitances of the two capacitors.

1/Ceq = 1/C1 + 1/C2

1.2 * 10^-6 = 1/C1 + 1/C2

We can solve for one capacitor in terms of the other:

C1 = Ceq / (2 - Ceq/C2)

Substituting this into the equation for the sum of the capacitances:

Ceq / (2 - Ceq/C2) + C2 = 5 * 10^-6

Solving for C2:

C2 = 3.3 * 10^-6 F

Substituting this back into the equation for C1:

C1 = 8.7 * 10^-7 F

Therefore, the capacitance of the two capacitors are 3.3 microfarads
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Read the following text and answer the following questions on the basis of the same:Supercapacitor: Super capacitor is a high capacity capacitor with a capacitance value much higher than normal capacitors but with lower voltage limits. Such capacitors bridges the gap between electrolytic capacitors and rechargeable batteries. In automobile, bus, train, crane, elevator such capacitors are used for regenerative braking, short term energy storage or burst-mode power delivery. Super capacitors have many advantages over batteries: they are very low weight and generally don't contain harmful chemicals or toxic metal. They can be charged and discharged innumerable number of times without ever wearing out. The disadvantage is that super capacitors aren’t well-suited for long-term energy storage. The discharge rate of super capacitors is significantly higher than lithium-ion batteries; they can lose as much as 10-20% of their charge per day due to self discharge.Super capacitor makes a bridge between

Two capacitor in series with 1000v of store of energy of 0.6J while the same two capacitor in parallel across the same sorce of 2.5 J .calculate the capacitance of each capacitor?
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Two capacitor in series with 1000v of store of energy of 0.6J while the same two capacitor in parallel across the same sorce of 2.5 J .calculate the capacitance of each capacitor? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Two capacitor in series with 1000v of store of energy of 0.6J while the same two capacitor in parallel across the same sorce of 2.5 J .calculate the capacitance of each capacitor? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two capacitor in series with 1000v of store of energy of 0.6J while the same two capacitor in parallel across the same sorce of 2.5 J .calculate the capacitance of each capacitor?.
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