How to Calculate the Charge Required to Store Energy in a Capacitor
How much charge must be transferred between the initially uncharged plates in order to store 18 mJ of energy?
What is the formula for calculating the charge required to store energy in a capacitor?
Answer:
To find the charge required to store 18 mJ in a parallel-plate capacitor, calculate the capacitor's capacitance with the given dimensions and then apply the formula for energy stored in a capacitor.
When dealing with a parallel-plate capacitor, the first step is to calculate the capacitance based on the dimensions provided. The formula for capacitance of a parallel-plate capacitor is C = ε_0(A/d), where ε_0 is the vacuum permittivity (8.85 ×10^{-12} F/m), A is the area of the plates, and d is the separation between the plates.
In this case, the plates are 5.0 cm on a side and spaced 1.2 mm apart. To calculate the capacitance C, we can use the formula C = ε_0(A/d).
Once the capacitance is determined, the energy stored in the capacitor can be calculated using the formula U = (1/2)CV^2, where U is the stored energy, C is the capacitance, and V is the voltage.
By rearranging the energy equation, we can find the charge Q needed to store 18 mJ of energy, using the relationship Q = √(2UC).