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Question:

 
Obtain the equivalent capacitance of the network in below Figure. For a 300 V supply, determine the charge and voltage across each capacitor.

Answer:

Capacitance of capacitor C1 is 100 pF.

Capacitance of capacitor C2 is 200 pF.

Capacitance of capacitor C3 is 200 pF.

Capacitance of capacitor C4 is 100 pF.

Supply potential, V = 300 V

Capacitors C2 and C3 are connected in series. Let their equivalent capacitance be C' .

Capacitors C1 and C' are in parallel. Let their equivalent capacitance be 

C" and C4 are connected in series. Let their equivalent capacitance be C.

Hence, the equivalent capacitance of the circuit is 

Potential difference across C" = V" 

Potential difference across C4 = V4

Charge on C4 is given by 

Q4= CV

Hence, potential difference, V1, across C1 is 100 V.

Charge on C1 is given by,

Q1 = C1V1

     = 100 x 10-12 x 100

     = 10-8 C

C2 and C3 having same capacitances have a potential difference of 100 V together. Since C2 and C3 are in series,

the potential difference across C2 and C3 is given by,

V2= V3 = 50 V

Therefore, charge on C2 is given by,

Q2 = C2V2

     = 200 x 10-12 x 50

     = 10-8 C

And charge on C3 is given by,

Q3 = C3V3

     = 200 x 10-12 x 50

     = 10-8 C

Hence, the equivalent capacitance of the given circuit is 


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