Finding kilowatt hours from parallel capacitors

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Homework Help Overview

The problem involves calculating the cost of charging a bank of parallel-connected capacitors to a specified voltage, focusing on the conversion of electrical energy stored in capacitors into kilowatt hours.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to use the relationship CV = Q to find charge and is exploring how to convert voltage to joules and then to kilowatt hours. Some participants suggest using energy formulas for capacitors, while others clarify the units of energy.

Discussion Status

The discussion is ongoing, with participants providing guidance on relevant formulas for energy stored in capacitors. There is a lack of consensus on the approach, as the original poster expresses uncertainty about the calculations and the implications of the parallel configuration.

Contextual Notes

The original poster notes the need to account for the total number of capacitors in the bank and is unsure how the parallel connection affects the calculations. There is also a mention of unit costs for energy, which may influence the final outcome.

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Please Help! Finding kilowatt hours from parallel capacitors

Homework Statement



A parallel-connected bank of 5.00 µF capacitors is used to store electric energy. What does it cost to charge the 2900 capacitors of the bank to 45,000 V, assuming a unit cost of $0.03 per kW·h?


Homework Equations



CV = Q
1 Joule = 2.77E-7 kWh
1 Volt = 1 Joule per Coulomb

The Attempt at a Solution


I'm not sure how to convert from Volts to Joules and then to kilowatt hours. I tried CV=Q to find the Coulombs, from where I wanted to find the number of Joules. If my thinking is correct, the 45,000 Volts means there are 45,000 Joules per Coulomb. When i multiplied 5E-6 times 45,000 to find Q my result was that the charge was only .225 C for one capacitor, which seems low. I'm not sure where to go from here, and I'm very unsure of how to convert from Volts to Joules to Kilowatt hours. I know at the end I need to remember to multiply my final result by 2900 for the number of capacitors. I also don't know how the fact they're connected by parallel plays into this.

Please help!
 
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Are you familiar with the formula E=1/2CV^2 or E=Q^2/2C? Those are the formulas for the energy stored in a capacitor.
 


Okay, i'll try that and see if i can work out the right answer
 
Last edited:


The units for E is in joules correct?
 


That depends on what you use for C, V, and Q. If you use standard SI units, E will come out in joules.
 

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