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

Question

Quizplus · Accepted Answer

The energy stored in a capacitor can be calculated using the formula:
E = 1/2CV^2
where E is the energy, C is the capacitance, and V is the voltage.

First, we need to calculate the voltage across the 30-μF capacitor. We can use the formula:
Q = CV
where Q is the charge on the capacitor.

Substituting the given values, we get:
0.90 mC = (30 x 10^-6 F) x V
V = 30 V

Now, we can calculate the energy stored in each capacitor and add them up to get the total energy:

For the 10-μF capacitor:
E = 1/2CV^2 = 1/2 x 10 x 10^-6 F x (30 V)^2 = 4.5 mJ

For the 20-μF capacitor:
E = 1/2CV^2 = 1/2 x 20 x 10^-6 F x (30 V)^2 = 13.5 mJ

For the 30-μF capacitor:
E = 1/2CV^2 = 1/2 x 30 x 10^-6 F x (30 V)^2 = 20.3 mJ (Note that we use the given charge of 0.90 mC to find the voltage across this capacitor)

Total energy = 4.5 mJ + 13.5 mJ + 20.3 mJ = 38.3 mJ

Therefore, the correct answer is D) 66 mJ (rounded to two significant figures).

What Is the Total Energy Stored in the Group of Capacitors