Final answer:
To calculate the energy stored in the capacitors, use the formula Energy = 0.5 * C * V^2. For the 2.0 microfarad capacitor with a potential difference of 3.00 volts, the energy is 9.0 x 10^-6 J. For the 4.0 microfarad capacitor with a potential difference of 3.00 volts, the energy is 36.0 x 10^-6 J. The total energy stored in the capacitors is 45.0 x 10^-6 J.
Step-by-step explanation:
To calculate the energy stored in the capacitors, we can use the formula:
Energy = 0.5 * C * V^2
Where C is the capacitance and V is the potential difference.
For the 2.0 microfarad capacitor:
- C = 2.0 x 10^-6 F
- V = 3.00 V
Plugging these values into the formula we get:
Energy = 0.5 * (2.0 x 10^-6 F) * (3.00 V)^2
Calculating this gives us:
Energy = 9.0 x 10^-6 J
For the 4.0 microfarad capacitor:
- C = 4.0 x 10^-6 F
- V = 3.00 V
Plugging these values into the formula we get:
Energy = 0.5 * (4.0 x 10^-6 F) * (3.00 V)^2
Calculating this gives us:
Energy = 36.0 x 10^-6 J
The total energy stored in the capacitors is the sum of these two values:
Total Energy = 9.0 x 10^-6 J + 36.0 x 10^-6 J
Calculating this gives us:
Total Energy = 45.0 x 10^-6 J