Electromagnetism - Capacitor

Two capacitors of capacitance 1.0 microfarad and 2.0 microfarad are each charged by being connected across a 5.0-Volt battery. They are disconnected from the battery and then connected to each other with resistive wires so that plates of opposite charge are connected together. What will be the magnitude of the final voltage across the 2.0 microfarad capacitor?

A. 0 V
B. 0.6 V
C. 1.7 V
D. 3.3 V
E. 5.0 V

(GR9677 #62)

Solution:

The charges stored at each capacitor:

Q₁ = C₁ × V_t = 1 × 5 = 5 μF
Q₂ = C₂ × V_t = 2 × 5 = μF

The plates of opposite charge are connected together (series connection):

Q₁'  =  Q₂' = Q_t
1/C_t  = 1/C₁  +  1/C₂ = 1  +  1/2 = 3/2
C_t = 2/3
Since  V_t = 5
Q₂' = Q_t  =  C_t × V_t = 2/3 × 5 = 10/3

→ V₂ = Q₂' / C₂ = 10/3 × 1/2 =  10/6 = 1.66 V

Answer: C