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CBSE Class 12 Physics 2017 Delhi Set 2 Paper

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Question : 5 of 8
Marks: +1, -0
A 12 pF12\ \mathrm{pF} capacitor is connected to a 50 V50\ \mathrm{V} battery. How much electrostatic energy is stored in the capacitor? If another capacitor of 6 pF6\ \mathrm{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 pF12\ \mathrm{pF} capacitor
Total charge stored in combination
Potential difference across each capacitor
Energy stored, in the capacitor of capacitance 12  pF\ \mathrm{pF} ,
U  =  12C1V2U\;=\;\frac{1}{2} C_1 V^2
  =  12×12×10−12×50×50 J\;=\;\frac{1}{2} \times 12 \times 10^{-12} \times 50 \times 50 \ \mathrm{J}
  =1.5×10−8 J\;=1.5 \times 10^{-8} \ \mathrm{J}
C=C= Equivalent capacitance of 12 pF12\ \mathrm{pF} and 6 pF6\ \mathrm{pF}, in series, is given by
    1C  eq   =  112+  16=  1+212\;\;\frac{1}{C_{\;\text{eq }\;}} = \;\frac{1}{12} + \;\frac{1}{6} = \;\frac{1+2}{12}
∴    C  eq     =4 pF\therefore \;\; C_{\;\text{eq }\;}\;=4\ \mathrm{pF}
∴\therefore Charge stored across each capacitor
q  =CeqVq\;=C_{e q} V
  =4×10−12×50 C\;=4 \times 10^{-12} \times 50\ \mathrm{C}
  =2×10−10 C\;=2 \times 10^{-10}\ \mathrm{C}
Charge on each capacitor 12 pF12\ \mathrm{pF} as well as 6 pF6\ \mathrm{pF}
∴\therefore Potential difference across capacitor C1C_1
∴V1=  2×10−1012×10−12   volt   =  503 V\therefore V_1=\;\frac{2 \times 10^{-10}}{12 \times 10^{-12}} \;\text{ volt }\;=\;\frac{50}{3}\ \mathrm{V}
Potential difference across capacitor C2C_2
∴V2=  2×10−106×10−12   volt   =  1003 V\therefore V_2=\;\frac{2 \times 10^{-10}}{6 \times 10^{-12}} \;\text{ volt }\;=\;\frac{100}{3}\ \mathrm{V}
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