In order to obtain a high value for capacitance, the permittivity of the dielectric medium should be?
A
Low
B
High
C
Zero
D
Unity

Question

In order to obtain a high value for capacitance, the permittivity of the dielectric medium should be?

Examoogle · Accepted Answer

High

Explanation: The capacitance of a parallel plate capacitor is directly proportional to the permittivity of the dielectric material placed between the plates. Increasing the permittivity allows for greater electrostatic energy storage for a given potential difference, thereby increasing the capacitance.

Working Principle: The capacitance is given by $C = \frac{\epsilon A}{d}$, where $\epsilon = \epsilon_0 \epsilon_r$ is the permittivity, $A$ is the area, and $d$ is the plate separation. A dielectric material with high relative permittivity (high dielectric constant) reduces the electric field strength within the dielectric by polarization, which permits more charge to be stored on the plates at the same voltage.

Key Formulas: $C = \frac{\epsilon_0 \epsilon_r A}{d}$ — Capacitance of a parallel plate capacitor; $\epsilon = \epsilon_0 \epsilon_r$ — Total permittivity of the medium

Key Points: Capacitance $C$ increases linearly with the permittivity $\epsilon$ of the dielectric medium.; Higher permittivity materials (like ceramics or high-K dielectrics) are used to manufacture high-value compact capacitors.; Vacuum has the lowest relative permittivity ($\epsilon_r = 1$), resulting in the lowest capacitance for a given geometry.

Advantages: Allows miniaturization of electronic circuits.; Higher energy density storage in capacitors.

Disadvantages: High permittivity materials often exhibit higher leakage currents.; May have higher dielectric loss (tan $\delta$) at high frequencies.

Applications: High-capacity decoupling capacitors in power supplies.; Memory storage elements in DRAM cells.

Additional Info: The relative permittivity $\epsilon_r$ is also known as the dielectric constant ($K$).. Option A is incorrect because low permittivity results in lower capacitance.. Option C is impossible as the permittivity of any physical medium is at least that of vacuum ($\epsilon_0 > 0$).

Answer: B is correct — High permittivity increases the electrostatic charge storage capacity of a capacitor for a given potential.

Exam Tip: Always remember the mnemonic 'C is directly proportional to epsilon' to solve geometry-based capacitance problems quickly.

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