A parallel plate capacitor with C=0.050 μF has a separation between its plates of d=50.0 μm . Th

step 1 Hi, in the given problem, the capacitance of a parallel plate capacitor has been given as 0 .050

A parallel plate capacitor with C=0.050 μF has a separation...

A parallel plate capacitor with $C=0.050 \mu \mathrm{F}$ has a separation between its plates of $d=50.0 \mu \mathrm{m} .$ The dielectric that fills the space between the plates has dielectric constant $\kappa=2.5$ and resistivity $\rho=4.0 \cdot 10^{12} \Omega \mathrm{m} .$ What is the time constant for this capacitor? (Hint: First calculate the area of the plates for the given $C$ and $\kappa$, and then determine the resistance of the dielectric between the plates.)

Key Concepts

Resistivity and Electrical Resistance of the Dielectric

The resistivity of a material is a measure of how strongly it resists the flow of electric current. In the context of a capacitor with a dielectric, the dielectric's resistivity along with its geometry (distance and area) determines the resistance through the material, using the relation R = ?d/A, where R is the resistance, ? is the resistivity, d is the separation, and A is the area.

RC Time Constant

The RC time constant is the product of the resistance (R) and the capacitance (C) in a circuit. It characterizes the rate at which the capacitor charges or discharges, with a larger time constant indicating a slower rate. This constant is crucial in understanding the dynamic behavior of circuits involving capacitors and resistors.

Dielectric Constant

The dielectric constant is a dimensionless property of a material that indicates its ability to reduce the effective electric field between the plates of a capacitor. It effectively increases the capacitance by a factor of ? compared to a vacuum, influencing how much electrical charge the capacitor can store.

Parallel Plate Capacitor

A parallel plate capacitor consists of two conducting plates separated by a distance, where its capacitance depends on the area of the plates, the separation distance, and the properties of the medium in between. When a dielectric material fills the space, the capacitance can be calculated using the formula C = ???A/d, where ? is the dielectric constant, ?? is the permittivity of free space, A is the area of the plates, and d is the separation between them.

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