Physics Class 12 NCERT Solutions: Chapter 2 Electrostatic Potential and Capacitance Part 3

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Series and Parallel capacitors

Series and Parallel Capacitors

Q: 6. Three capacitors each of capacitance are connected in series.

(A) What is the total capacitance of the combination?

(B) What is the potential difference across each capacitor if the combination is connected to a supply?

Answer:

(A) Capacitance of each of the three capacitors,

Equivalent capacitance (C) of the combination of the capacitors is given by the relation,

Therefore, total capacitance of the combination is .

(B) Supply voltage,

Potential Difference (V) across each capacitor is equal to one-third of the supply voltage.

Therefore, the potential difference across each capacitor is .

Q: 7. three capacitors of capacitances are connected in parallel.

(A) What is the total capacitance of the combination?

(B) Determine the charge on each capacitor if the combination is connected to a supply.

Answer:

(A) Capacitances of the given capacitors are

For the parallel combination of the capacitors, equivalent capacitor is given by the algebraic sum,

Therefore, total capacitance of the combination is .

(B) Supply voltage,

The voltage through all the three capacitors is same

Charge on a capacitor of capacitance C and potential difference V is given by the relation,

,

Charge

Charge

Charge

Q: 8. In a parallel plate capacitor with air between the plates, each plate has an area of and the distance between the plates is . Calculate the capacitance of the capacitor. If this capacitor is connected to a supply, what is the charge on each plate of the capacitor?

Answer:

Area of each plate of the parallel plate capacitor,

Distance between the plates,

Supply voltage,

Capacitance C of a parallel plate capacitor is given by,

Where,

Permittivity of free space

Potential V is related with the charge q and capacitance C as

Therefore, capacitance of the capacitor is and charge on each plate is .