Total energy in a circuit – physics?

Question

What is the total energy stored in the group of capacitors shown if the charge on the 30-µF capacitor is 0.90 mC? I have included a picture of the circuit for reference: http://bayimg.com/caMlHaaEH. The answer I found is 66 mJ. Thank you in advance for your help!

Anonymous · Accepted Answer

What is the total energy stored in the group of capacitors shown if the charge on the 30-µF capacitor is 0.90 mC?

Picture of circuit: http://bayimg.com/caMlHaaEH

Answer: 66 mJ

Let’s determine the energy of the 30-µF capacitor.

http://hyperphysics.phy-astr.gsu.edu/hbase/electri...

The equation below is from the website above. I also found this equation in my college physics book.

Energy = Q^2 ÷ (2 C) = (0.9 10^-3)^2 ÷ 60 10^-6 = 1.35 10^-2 J

Let’s determine the voltage of the 30-µF capacitor.

C = Q ÷ V, V = Q ÷ C

V = 0.9 10^-3 ÷ 30 10^-6 = 30 volts

Since the 15 μF capacitor is in parallel with the 30 μF capacitor, the voltage is the same for both capacitors.

Energy = ½ C V^2 = ½ 15 10^-6 30^2 = 6.375 10^-3

When capacitors are in series, the charge is the same. Let’s determine the charge on the 15 μF capacitor.

C = Q ÷ V, Q = C * V

Q = 15 10^-6 30 = 4.5 * 10^-4 C

Total charge of parallel capacitors = 0.9 10^-3 + 4.5 10^-4 = 1.35 * 10^-3

Since the 20 μF capacitor is in series with the other capacitors, the charge of it is 1.35 * 10^-3.

Energy = Q^2 ÷ (2 C) = (1.35 10^-3)^2 ÷ 40 10^-6 = 4.55625 10^-2

Total energy = 1.35 10^-2 + 6.375 10^-3 + 4.55625 10^-2 = 6.54375 10^-2 J

The total energy is 0.065375 joules

This rounds to 66 mJ!

Anonymous

Total energy in a circuit – physics?

1 Answers

AI-Powered Insights

Want to answer this question?

Categories

Tags

Related Questions