Two identical capacitors store different amounts of energy: capacitor A stores 2.5 x 10^-3 J, and capacitor B stores 4.8 x 10^-4 J. The voltage across the plates of capacitor B is 12 V. Find the voltage across the plates of capacitor A.
To find the voltage across the plates of capacitor A, we can use the formula for the energy stored in a capacitor:
Energy = (1/2) * C * V^2
Where:
- Energy is the amount of energy stored in the capacitor
- C is the capacitance of the capacitor
- V is the voltage across the plates of the capacitor
In this case, we are given:
- Energy for capacitor A: 2.5 x 10^-3 J
- Energy for capacitor B: 4.8 x 10^-4 J
- Voltage for capacitor B: 12 V
Let's calculate the voltage across the plates of capacitor A:
Step 1: Calculate the capacitance of capacitor B
Since we have the energy and voltage for capacitor B, we can rearrange the formula to solve for the capacitance:
C = 2 * Energy / V^2
Plugging in the values:
C = 2 * (4.8 x 10^-4 J) / (12 V)^2
C = 8 x 10^-5 J / 144 V^2
C = 5.56 x 10^-7 Farads
Step 2: Calculate the voltage across the plates of capacitor A
Now that we have the capacitance value for capacitor B, we can rearrange the formula to solve for the voltage:
Voltage = sqrt(2 * Energy / C)
Plugging in the values:
Voltage = sqrt(2 * (2.5 x 10^-3 J) / (5.56 x 10^-7 Farads))
Using a calculator, we can calculate the voltage to be approximately 15.91 V.
Therefore, the voltage across the plates of capacitor A is approximately 15.91 V.