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NEET 2022
Exam
NEET
Year
2022
Subject
Physics
Chapter
Capacitance

NEET 2022 · Physics · Capacitance

A capacitor of capacitance C = 900pF is charged fully by 100V...

A capacitor of capacitance C=900pFC = 900pF is charged fully by 100V100V battery BB as shown in figure (a). Then it is disconnected from the battery and connected to another uncharged capacitor of capacitance C=900pFC = 900pF as shown in figure (b). The electrostatic energy stored by the system (b) is

A capacitor of capacitance C = 900pF is charged fully by 100V battery B as shown in figure (a). Then it is disconnected

Options

  1. A3.25×10−6J3. 25 \times {10}^{- 6}J
  2. B2.25×10−6J2. 25 \times {10}^{- 6}J
  3. C1.5×10−6J1. 5 \times {10}^{- 6}J
  4. D4.5×10−6J4. 5 \times {10}^{- 6}J

Correct answer

B. 2.25×10−6J2. 25 \times {10}^{- 6}J

Step-by-step solution

Initial charge on 900pF900pF capacitor will be q=CVq = CV

When the two equal capacitors are joined together as shown in figure (b). The charge will be equally divided among them. Therefore,

q′=q2=CV2q^{'} = \dfrac{q}{2} = \dfrac{CV}{2}

Now the energy stored in them will be

E=(q′)22C+(q′)22CE = \dfrac{\left(q^{'}\right)^{2}}{2C} + \dfrac{\left(q^{'}\right)^{2}}{2C}

⇒E=(CV2)2×1C=CV24=900×10−12×(100)24⇒ E = \left(\dfrac{CV}{2}\right)^{2} \times \dfrac{1}{C} = \dfrac{CV^{2}}{4} = \dfrac{900 \times {10}^{- 12} \times \left(100\right)^{2}}{4}

⇒E=2.25×10−6J⇒ E = 2. 25 \times {10}^{- 6}J

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