A certain capacitor stores 473 J of energy when it holds 7.91 x 10−2 C of charge. What is the capacitance of this capacitor?
What is the potential difference across the plates?
To find the capacitance of the capacitor, we can use the formula:
C = Q / V
where C is the capacitance, Q is the charge stored in the capacitor, and V is the potential difference across the plates.
Given that the capacitor stores 473 J of energy when it holds 7.91 x 10^-2 C of charge, we can determine the potential difference across the plates using the formula for energy stored in a capacitor:
E = 1/2 * C * V^2
Here, E is the energy stored in the capacitor, C is the capacitance, and V is the potential difference.
We know that E = 473 J and Q = 7.91 x 10^-2 C, so we can substitute these values into the energy formula:
473 J = 1/2 * C * V^2
Now, let's solve this equation for V:
473 J = 1/2 * C * V^2
Divide both sides of the equation by 1/2 to isolate the term with V^2:
946 J = C * V^2
We know that Q = C * V, so we can substitute Q = 7.91 x 10^-2 C into the equation:
946 J = (7.91 x 10^-2 C) * V
Now, solve for V:
V = 946 J / (7.91 x 10^-2 C)
Calculating this, we can find the value of V. Once we have V, we can substitute the values of Q and V into the formula for capacitance (C = Q / V) to find the capacitance of the given capacitor.