For the capacitor network shown in the figure the potential

For the capacitor network shown in the figure the potential difference across ab is 12.0 V. Part A Find the total energy stored in this network. Part B Find the energy stored in the 4.08-muF capacitor.

Solution

A)

Equivalent capacitance of the network:

Ceq = ( 8.6 || 4.8 ) || (6.2 || 11.8 + 3.5)

= (8.6*4.8/(8.6+4.8)) || (6.2*11.8/(6.2+11.8) + 3.5)

= 3.08 || (4.06 + 3.5)

= 3.08 || 7.56

= 3.08*7.56/(3.08+7.56)

= 2.19 uF

So, total energy stored in the network:

Utot = 0.5*Cnet*V^2

= 0.5*2.19*10^-6*12^2

= 1.58*10^-4 J

= 158 uJ

B)

Charge stored in the network :

Q = Cnet*V

= 2.19*10^-6*12

= 2.63*10^-5 C

So, energy stored in the 4.8 uF capacitor :

U = 0.5*Q^2/C

= 0.5*(2.63*10^-5)^2/(4.8*10^-6)

= 7.21*10^-5 J

= 72.1 uJ