A dielectric material is introduced into the empty space between the two plates of a parallel plate capacitor. How will the capacitance (C) change if the value of the dielectric constant (κ) for the material is 1.5?

Question

A dielectric material is introduced into the empty space between the two plates of a parallel plate capacitor.  How will the capacitance (C) change if the value of the dielectric constant (κ) for the material is 1.5?

Quizplus · Accepted Answer

11ecba2d_1306_a60c_a3bf_159a93772661_MD0008_00 A capacitor is a device that stores electrical charge between equally but oppositely charged conductive surfaces (plates) separated by a fixed distance (d). Capacitor strength is determined by the quantity of charge (Q) stored on each plate relative to the voltage (V), or attractive electric potential energy, this separation of charges generates. Capacitor strength is quantified by capacitance (C), a variable generally given in units of farads (F) and calculated using: 11ecba2d_1306_a60d_a3bf_b591ce3eff2b_MD0008_00 In the case of a simple parallel plate capacitor, capacitance is determined largely by physical dimensions and plate material. However, dielectrics can be inserted between capacitor plates such that the characteristics of a capacitor are altered. Dielectrics are a class of polarizable materials in which electric dipoles can be induced. When a dielectric material is inserted between capacitor plates, the electric field present between these plates causes the dipoles induced in the dielectric material to align, decreasing both electric field strength and voltage. Due to this insulating effect, dielectric substances increase capacitance. Accordingly, the dielectric constant (κ) reflects the ability of dielectrics to increase the functional capacitance beyond the capacitance in a vacuum (C₀), defined as the absence of any material. This relationship is expressed as: 11ecba2d_1306_a60e_a3bf_b1bc4ef64b50_MD0008_00 In this question, a dielectric material with a dielectric constant of 1.5 is introduced into the previously empty space of a parallel plate capacitor under vacuum. Applying the above equation, the new capacitance following the addition of the dielectric material can be calculated as: 11ecba2d_1306_a60f_a3bf_ebf76bcbf631_MD0008_00 Therefore, introducing a dielectric with a dielectric constant of 1.5 will increase capacitance by 50% (Choice C). (Choices A and B) Both a vacuum and dielectric materials have κ values that are greater than 1. As such, introducing any material with κ ≥ 1 must increase capacitance. (Choice D) A material with a κ value of 2 would have to be introduced between capacitor plates for capacitance to increase 100%. However, the dielectric used in this question has a κ value of only 1.5. Educational objective: A dielectric can be introduced between the plates of a parallel plate capacitor to cause an increase in capacitance. The dielectric constant κ measures the ability of a dielectric material to increase capacitance.

A Dielectric Material Is Introduced into the Empty Space Between