Question

Two capacitors C₁ =1µF and C₂= 4µF are charged to a potential difference of 100 volts and 200 volts respectively. The charged capacitors are now connected to each other with terminals of opposite sign connected together. What is the 

(a) Final charge on each capacitor in steady state? 

(b) Decrease in the energy of the system?

Answer 1

The capacitors are connected parallel to each other. 

Thus the equivalent capacitance is given by C = C₁ +C₂. 

The charges stored in capacitor is given by Q = CV. The energy stored in each capacitor is given by

U = 1/2 CV².

When the terminals of opposite polarity are connected together, the magnitude of net charge finally is equal to the difference of magnitude of charges before connection.

Let V be the final common potential difference across each.

The charges will be redistributed and the system attains a steady state when potential difference across each capacitor becomes same.

Note that because C₁ V₁  < C₂ V₂, the final charge polarities are same as that of C₂ before connection. 

Loss of energy

Note: the energy is lost as heat in the connected wires due to the temporary currents that flow while the charge is being redistributed.