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Question : 5
Total: 8
A 12 pF capacitor is connected to a 50 V battery. How much electrostatic energy is stored in the capacitor? If another capacitor of 6 pF is connected in series with it with the same battery connected across the combination, find the charge stored and potential difference across each capacitor.
Solution:
Calculation of electrostatic energy in 12 pF capacitor
Total charge stored in combination
Potential difference across each capacitor
Energy stored, in the capacitor of capacitance 12pF ,
U =
C 1 V 2
=
× 12 × 10 − 12 × 50 × 50 J
= 1.5 × 10 − 8 J
C = Equivalent capacitance of 12 pF and 6 pF , in series, is given by
=
+
=
∴ C eq = 4 pF
∴ Charge stored across each capacitor
q = C e q V
= 4 × 10 − 12 × 50 C
= 2 × 10 − 10 C
Charge on each capacitor12 pF as well as 6 pF
∴ Potential difference across capacitor C 1
∴ V 1 =
volt =
V
Potential difference across capacitorC 2
∴ V 2 =
volt =
V
Total charge stored in combination
Potential difference across each capacitor
Energy stored, in the capacitor of capacitance 12
Charge on each capacitor
Potential difference across capacitor
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