CBSE Class 12 Physics 2017 Delhi Set 2 Paper

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Question : 5
Total: 8
A 12‌pF capacitor is connected to a 50V battery. How much electrostatic energy is stored in the capacitor? If another capacitor of 6‌pF 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 12‌pF capacitor
Total charge stored in combination
Potential difference across each capacitor
Energy stored, in the capacitor of capacitance 12 pF ,
U‌=‌
1
2
C1
V2

‌=‌
1
2
×12
×10−12
×50
×50J

‌=1.5×10−8J
C= Equivalent capacitance of 12‌pF and 6‌pF, in series, is given by
‌‌
1
C‌eq ‌
=‌
1
12
+‌
1
6
=‌
1+2
12

∴‌‌C‌eq ‌‌=4‌pF
∴ Charge stored across each capacitor
q‌=CeqV
‌=4×10−12×50C
‌=2×10−10C
Charge on each capacitor 12‌pF as well as 6‌pF
∴ Potential difference across capacitor C1
∴V1=‌
2×10−10
12×10−12
‌ volt
‌
=‌
50
3
V

Potential difference across capacitor C2
∴V2=‌
2×10−10
6×10−12
‌ volt
‌
=‌
100
3
V
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