NCERT Class XII Chapter
Electrostatic Potential and Capacitance
Questions With Solutions

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Question : 25
Total: 37
Obtain the equivalent capacitance of the network in figure. For a 300 V supply, determine the charge and voltage across each capacitor.

Solution:  
Since C2 and C3 are in series, so, C' = 100 pF
Since C1 and C' are parallel
so C" = C1 + C' = 100 + 100 or C" = 200 pF
Since C4 and C" are in series, so net capacitance of the network is
1
C
=
1
C"
+
1
C4
=
1
200
+
1
100
=
1+2
200
or C2 =
200
3
pF = 66.7 pF
Net charge stored on the combination is
Q = CV =
200
3
× 1012 × 300 = 2 × 108 C
As C″ and C4 are in series, so Q" = Q4 = Q or Q" = Q4 = 2 × 108 C
and hence V" =
Q"
C"
=
2×108C
200×1012F
= 100 V
and V4 =
Q4
C4
=
2×108C
100×1012F
= 200 V
Since C1 and C' are in parallel, so
V1 = V' = V" or V1 = V' = 100 V
and hence Q1 = C1V1 = 100 × 1012 × 100 = 1 × 108 C
and Q' = C1V1 = 100 × 1012 × 100 = 1 × 108 C
and Q' = C'V' = 100 × 1012 × 100 = 1 × 108 C
Since C2 and C3 are in parallel, so Q2 = Q3 = Q' or Q2 = Q3 = 1 × 108 C and hence V2 =
Q2
C2
=
1×108C
200×1012F
= 50 V
and V3 =
Q3
C3
=
1×108C
200×1012F
= 50 V
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