Question

a capacitor of 200pF is charged by 300V battery. the battery is then disconnected and the charged capacitor is connected to another uncharged capacitor of 100pF . calculate the difference in the energy stored ?
please answer urgent......

Answer 1

when a charged capacitor is connected with another uncharged capacitor , then charge transfer from charged capacitor to uncharged capacitor untill both attend same potential .

now, A capacitor of capacitance 200 pF charged by 300V battery
Means charge on this capacitor = CV = 200 × 300 pC = 6 × 10⁴ pC

Now, charged capacitor of charge 6 × 10⁴ pC is connected with uncharged capacitor . Let final potential of both capacitors is V
Then, intial charge = final charge
6 × 10⁴ pC = 200 × V + 100 × V
V = 200 V
Hence, final potential is 200V

Now, energy stored intially on capacitor of 200pF = 1/2 CV²
= 1/2 × (200pF)×( 300V )²
= 100 × 10⁻¹² × 90000 J
= 9 × 10⁻⁶ J
Finally energy stored in both capacitors = 1/2(C + C')V²
= 1/2 × (200pF + 100pF) × (200V)²
= 150 × 10⁻¹² × 40000
= 6 × 10⁻⁶ J

Hence, difference in energy stored = intial energy - final energy
= 9 × 10⁻⁶ J - 6 × 10⁻⁶ J = 3 × 10⁻⁶J

Answer 2

There is transfer of charges whenever an unchanged capacitor and a charged capacitor and put in contact.

We therefore need to calculate the charge in the capacitors.

Before doing the calculations, we can state important conversions which are sensitive in our calculations.

These are:

1 microfarad = 1000000 picofarads

1 farad = 1000000 microfarads

Farads are units of measurements for Capacitance.

CALCULATIONS

Q=CV where Q is the charge in coulombs, C Capacitance in farads and voltage in volts.

Let Capacitor with 200pF be A and one with 100pF be B

Charge on A is:

200×300=60000 pCoulombs

When these two capacitors are brought together there will be transfer of charges such that a uniform potential is achieved.

Let final potential =V

Initial charge=final charge

60000pC =200V + 100V

300V=60000

V=200

Energy stored by capacitor =1/2 × C×V^2

Initial energy =0.5 × 200 ×300×300=9000000pJ

Convert to joules using the conversions stated above.

900000 × 10^-12
= 9× 10^-6 Joules

Final energy = 1/2(100+200) × 200×200=6000000pJoules

Converting:

6 × 10^-6

The difference in energy stored is equal to: Initial energy - final energy.

(9 ×10^-6) - (6× 10^-6)= 3 × 10^-6Joules.