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What has a larger capacitance, an aluminum sphere with a 10 cm diameter or one with a 100 cm diameter? Question 16 options: 10 cm 100 cm They are both the same. cannot be determined

Answer :

[tex]\boxed{\sf C=\dfrac{Q}{V}}[/tex]

But

[tex]\boxed{\sf \Delta V_{R_2\to R_1}={\displaystyle{\int}^{R_1}_{R_2}}dV=-{\displaystyle{\int}^{R_1}_{R_2}}\dfrac{kQ}{r^2}dR}[/tex]

  • Hence higher the radius lower the voltage
  • Lower the voltage higher the capacitance .

100cm diameter having aluminium sphere has a larger capacitance

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