Question

Two insulated metallic spheres of 3 microfarad and 5 microfarad capacitance are charged to 300v and 500 v the energy loss when they are connected by wire is

Answer 1

Answer:

here is ur answer ......

Answer 2

The energy loss is 0375J

Capacitance of sphere one = C1 = 3 = 3 ×10-6F

Capacitance of sphere two = C2 = 5 = 5 ×10-6F

Voltage one = V1 = 300 volt

Voltage two = V2 = 500 volt

Initial Electrostatic energy of the capacitor -

Ui = 1/2 C1V1² + 1/2C2V2²

Ui = 1/2 × 3 ×10-6 × (300)2 + 1/2×5 ×10-6 × (500)2

= 76×10-2J

Total capacitance -  

C = C1 + C2 = 3 ×10-6 + 5 ×10-6

= 8×10-6 F

Charge in the capacitors

Q = C1V1+C2V2

Q = 3 ×10-6×300 + 5 ×10-6×500

= 34×10-4 C

Let V be the common potential of the capacitors after connection

V = Q/C

V = 34 × 10-4/ 8 × 10-6

=  425 volt

Final electrostatic energy -

Uf = 1/2CV² = 1/2 × 8 × 10-6× (425)²

= 7225×10-4 J

Loss in energy in form of heat -  

Ui - Uf = 76×10-2-7225 ×10-4 J

=7600×10-4-7225 ×10-4 J

= 375 ×10-4J

= .0375