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Obtain the Equivalent Capacitance of the Network and Determine the Charge and Voltage Across Each Capacitor. - Physics

Obtain the equivalent capacitance of the network in Fig. 2.35. For a 300 V supply, determine the charge and voltage across each capacitor.

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Solution

Capacitance of capacitor Cis 100 pF.

Capacitance of capacitor Cis 200 pF.

Capacitance of capacitor Cis 200 pF.

Capacitance of capacitor Cis 100 pF.

Supply potential, V = 300 V

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

`therefore 1/C'=1/200+1/200=2/200`

`therefore C'=100 pF`

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

 `therefore C''=C'+C_1`

`=100+100=

200 pF`

C'' and `C_4` are connected in series. Let their equivalent capacitance be C.

`therefore 1/C=1/(C'')+1/(C_4)`

`=1/200+1/100=(2+1)/200`

`C=200/3 pF`

Hence, the equivalent capacitance of the circuit is `200/3 pF`

Potential difference across C"=V"

Potential difference across C4 = V4

`therefore V''+V_4=V=300V`

Charge on `C_4` is given by

Q4CV

`=200/3xx10^-12xx300`

`=2xx10^-8 C`

`therefore V_4=Q_4/C_4`

`=(2xx10^-8)/(100xx10^-12)=200V`

Voltage across `C_1` is given by

`V_1=V-V_4`

`300-200=100V`

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

Charge on C1 is given by,

`Q_1=C_1V_1`

`=100xx10^-12xx100`

`=10^-8 C`

C2 and C3 having same capacitances have a potential difference of 100 V together. Since C2 and C3are in series, the potential difference across Cand Cis given by,

V2 = V3 = 50 V

Therefore, charge on C2 is given by,

`Q_2=C_2V_2`

`=200xx10^-12xx50`

`=10^-8 C`

And charge on C3 ­is given by,

`Q_3=C_3V_3`

`=200xx10^-12xx50`

`=10^-8 C`

Hence, the equivalent capacitance of the given circuit is `200/3pF` with 

`Q_1=10^-8C,`         `V_1=100V`

`Q_2=10^-8`            `V_2=50V`

`Q_3=10^-8C,`        `V_3=50V`

`Q_4=2xx10^-8C,`   `V_4=200V`

Concept: Capacitors and Capacitance
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APPEARS IN

NCERT Class 12 Physics Textbook
Chapter 2 Electrostatic Potential and Capacitance
Q 25 | Page 90
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