- #1
JosephK
- 40
- 2
Homework Statement
A charge Q is placed on a capacitor of capacitance C. The capacitor is connected into the circuit as shown in the figure below, with an open switch, a resistor, and an initially uncharged capacitor of capacitance 3C. The switch is then closed and the circuit comes to an equilibrium.
(a) find the final potential difference between the plates of each capacitor.
(b) Find the charge on each capacitor.
(c) Find the final energy stored in each capacitor.
(d) Find the internal energy appearing in the resistor.
Homework Equations
E = 1/2 C ΔV^2
U = QΔV
The Attempt at a Solution
As we move across the charged capacitor from negative to positive, the capacitor increases the electric potential energy by exactly E= 1/2 C V^2. Energy is delivered to the resistor and the uncharged capacitor.
Conservation of energy:
[itex] 1/2 C(\Delta V_C^{2})= Q(\Delta V_R) + 1/2 (3C)(\Delta V_{3C}^{2})[/itex]
In equilibrium, [itex]V_C = V_R+V_{3C}[/itex]
Where V_C, V_R and V_C is the voltage across the initially charged capacitor, resistor, and initially uncharged capacitor respectively.