Q79 / 110 · VITEEE 2022 · Physics

A capacitor \(\mathrm{C}_1\) is charged to a potential difference \(\mathrm{V}\). The charging battery is then removed and the capacitor is connected to an uncharged capacitor \(\mathrm{C}_2\). The potential difference across the combination is

  • Correct answer
    A
    \(\frac{\mathrm{VC}_1}{\left(\mathrm{C}_1+\mathrm{C}_2\right)}\)
  • B
    \(\mathrm{v}\left(1+\frac{\mathrm{C}_2}{\mathrm{C}_1}\right)\)
  • C
    \(\mathrm{V}\left(1+\frac{\mathrm{C}_1}{\mathrm{C}_2}\right)\)
  • D
    \(\frac{\mathrm{VC}_2}{\left(\mathrm{C}_1+\mathrm{C}_2\right)}\)

Solution

Charge \(\mathrm{Q}=\mathrm{C}_1 \mathrm{~V}\) Total capacity of combination (parallel) \(\mathrm{C}=\mathrm{C}_1+\mathrm{C}_2\) \(\text {P.D. }=\frac{\mathrm{Q}}{\mathrm{C}}=\frac{\mathrm{C}_1 \mathrm{~V}}{\mathrm{C}_1+\mathrm{C}_2}\)

Hence, the correct answer is option: 'A'.

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