Capacitance

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Filling the gap of an air capacitor completely with a material of dielectric constant 4 changes its ability to store charge, so what is the effect on capacitance?

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Filling a capacitor with a dielectric multiplies its capacitance by the dielectric constant, so $C = \kappa C_0$, a relationship established in NCERT Class 12, Chapter 2 (Electrostatic Potential and Capacitance). The dielectric reduces the effective field for a given charge, which lowers the voltage and thereby raises the capacitance $C = Q/V$. With $\kappa = 4$ the new capacitance is four times the air value $C_0$. The option of one quarter is wrong because dielectrics always increase, never decrease, capacitance. The option that it stays the same is wrong because that would mean the dielectric has no effect, contradicting polarisation physics. The option of sixteen times is wrong because it mistakenly squares the dielectric constant. A physical and magnitude check confirms the factor of four: since the dielectric weakens the internal field by $\kappa$ and hence the voltage by $\kappa$ at fixed charge, the ratio $Q/V$ grows by exactly $\kappa$, giving a positive enhancement consistent with capacitors being deliberately filled with dielectrics to store more charge.

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