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Electrostatic Potential And Capacitance

Question
CBSEENPH12039102

Figure shows two identical capacitors, C1 and C2, each of 1 μF capacitance connected to a battery of 6 V. Initially switch 'S' is closed. After sometime 'S' is left open and dielectric slabs of dielectric constant K = 3 are inserted to fill completely the space between the plates of the two capacitors. How will the (i) charge and (ii) potential difference between the plates of the capacitors be affected after the slabs are inserted? 
                          

Solution

When switch S is closed, potential difference across capacitor is 6V
Potential across the battery, V1 = V2 = 6V

Capacitance of the capacitor, C1 = C2 = 1 straight mu space straight C
Charge on each capacitor, straight q subscript 1 space equals straight q subscript 2 space equals space CV space equals space left parenthesis 1 μF right parenthesis cross times left parenthesis 6 straight V right parenthesis space equals space 6 μC
When switch S is opened, the potential difference across C1 remains 6 V, while the charge on capacitor C2 remains 6 straight mu space straight C. After insertion of dielectric between the plates of each capacitor, the new capacitance of each capacitor becomes

C subscript 1 apostrophe space equals space C subscript 2 apostrophe space equals space 3 cross times 1 space mu F space equals space 3 space mu F 
i)

Now, charge on capacitor C1 ,q1’ = C1’V1 = 3 cross times 6 space equals space 18 space mu C
Charge on capacitor C2 remains the same, i.e., 6 straight mu space straight C

ii)
Potential difference across C1 remains the same.

Potential difference across Cis, V subscript 2 apostrophe space equals space fraction numerator q subscript 2 over denominator C subscript 2 apostrophe end fraction equals 6 over 3 equals space 2 space V

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