Final Answer:
The equation for capacitance when substituted into the capacitance + dielectric equation is ( C' = frac{C}{k} ), where ( C' ) is the new capacitance with the dielectric, ( C ) is the original capacitance without the dielectric, and ( k ) is the relative permittivity (dielectric constant) of the material.
Step-by-step explanation:
When a dielectric material is introduced between the plates of a capacitor, it affects the capacitance of the system.
The relationship between the capacitance with the dielectric ( C' )), the original capacitance without the dielectric ( C ), and the relative permittivity of the material ( k ) is defined by the equation C' = frac{C}{k} .
Capacitance is a measure of a capacitor's ability to store charge, and it depends on the physical characteristics of the capacitor.
such as the area of the plates, the distance between them, and the dielectric material between the plates.
The dielectric constant (\( k \)) represents the ability of the dielectric to permit the electric field between the plates, affecting the overall capacitance.
By substituting ( C' = frac{C}{k}) into the capacitance + dielectric equation, you can determine the new capacitance when a dielectric material is introduced, providing insight into how the presence of the dielectric alters the capacitor's ability to store charge.