What physical quantities may $X$ and $Y$ represent? ($Y$ represents the first mentioned quantity)

  • A
    Pressure $v/s$ temperature of a given gas (constant volume)
  • B
    Kinetic energy $v/s$ velocity of a particle
  • C
    Capacitance $v/s$ charge to give a constant potential
  • D
    Potential $v/s$ capacitance to give a constant charge

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$A$ capacitor of capacity $C$ is connected to a battery of potential $V$ in parallel. The distance between its plates is reduced to half at once,while the battery remains connected. Then,the energy supplied by the battery to charge the capacitor to potential $V$ again is:

Two parallel plate capacitors with capacitances $C$ and $2C$ are connected in parallel. They are charged to a potential difference $V$. Now,if the battery is disconnected and a dielectric of dielectric constant $K$ is inserted between the plates of the capacitor with capacitance $C$,find the potential difference across each capacitor.

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The charge on any one of the $2\,\mu F$ capacitors and the $1\,\mu F$ capacitor will be given respectively (in $\mu C$) as

The distance between the plates of a parallel plate capacitor is $5d$. The positively charged plate is at $x=0$ and the negatively charged plate is at $x=5d$. Two slabs,one of a conductor and the other of a dielectric,both of equal thickness $d$,are inserted between the plates as shown in the figure. The potential versus distance graph will look like:

Two metal spheres,one of radius $R$ and the other of radius $2R$,both have the same surface charge density $\sigma$. They are brought in contact and then separated. What will be the new surface charge densities on them?

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