Question:
A parallel plate capacitor has capacitance $C$. If it is equally filled the parallel layers of materials of dielectric constant $K_1$ and $K_2$ its capacity becomes $C_1$. The ratio of $C_1 $ and $C$ is
A parallel plate capacitor has capacitance $C$. If it is equally filled the parallel layers of materials of dielectric constant $K_1$ and $K_2$ its capacity becomes $C_1$. The ratio of $C_1 $ and $C$ is
Updated On: Apr 15, 2024
- $K_1 + K_2 $
- $\frac{K_1 K_2}{K_1 + K_2}$
- $\frac{K_1 + K_2}{K_1 K_2}$
- $\frac{2 K_1 K_2}{K_1 + K_2}$
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The Correct Option is D
Solution and Explanation
$C_{A} = \frac{K_{1} \varepsilon_{0}A}{\frac{d}{2}} , C_{B} = \frac{K_{2}\varepsilon_{0}A}{\frac{d}{2}} $
$C_{eq} = \frac{C_{1}}{C_{2}} = \frac{2K_{1}K_{2}}{K_{1} + K_{2}}$
$ = \frac{C_{A}C_{B}}{C_{A} + C_{B}} = \left(\frac{2K_{1} K_{2}}{K_{1} + K_{2}}\right) \frac{\varepsilon_{0}A}{d} $
$\left( \because e = \frac{\varepsilon_{0}A}{d}\right) $
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Concepts Used:
Capacitor
Capacitors commonly known as Condensers are passive components, similar to a resistor. In capacitors, charges are usually stored in the form of an "electrical field". Electrical and electronic circuits depend on the same which is made up of two parallel metal plates that are not connected to one another. The two plates are separated by a non-conducting insulating medium called dielectric.
Uses of Capacitors:
- DC blocking capacitors block the DC and allows only AC to certain parts of the circuit.
- These are main elements of filters.
- They possess the ability to couple a section of the circuit to another.
Types of Capacitors:
- Ceramic capacitors are created by covering two sides of their tiny ceramic disc with silver and stacking them together.
- Film Capacitors are commonly used capacitors that are made up of different sets of capacitors.
- In an electrolytic capacitor metallic anode coated with an oxidized layer used as a dielectric.
- A Paper capacitor is also known as a fixed capacitor in which paper is used as the dielectric material.
Read More: Types of Capacitors