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JEE Main 2023 (30 Jan, Shift 1) · Charge Sharing & Loss of Energy

Charge Sharing & Loss of Energy question from JEE Main 2023 (30 Jan, Shift 1)

Q17JEE Main 2023 · 30 JAN · SHIFT 1Medium

Charge Sharing & Loss of Energy

A capacitor of capacitance 900 μF900\ \mu\text{F} is charged by a 100 V100\text{ V} battery. The capacitor is disconnected from the battery and connected to another uncharged identical capacitor such that one plate of uncharged capacitor connected to positive plate and another plate of uncharged capacitor connected to negative plate of the charged capacitor. The loss of energy in this process is measured as x×10−2 Jx\times 10^{-2}\text{ J}. The value of xx is _____________.

Numerical answer type. Work it out, then open the answer.

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Answer: 225

  1. The uncharged capacitor is simply put across the charged one, i.e. in parallel with it.
  2. For identical capacitors, loss =14CV2=14×900×10−6×1002=2.25= \frac{1}{4}CV^2 = \frac{1}{4} \times 900 \times 10^{-6} \times 100^2 = 2.25 J
  3. 2.252.25 J =225×10−2= 225 \times 10^{-2} J, so x=225x = 225.
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