Question:
The energy stored in a parallel plate capacitor of cross section area $ A $ with a separation $ d $ being filled with dielectric of dielectric constant $ \varepsilon_{0} $ in terms of the electric field between them, $ E $ is
The energy stored in a parallel plate capacitor of cross section area $ A $ with a separation $ d $ being filled with dielectric of dielectric constant $ \varepsilon_{0} $ in terms of the electric field between them, $ E $ is
Updated On: Jul 29, 2022
- $ \frac{1}{2} \varepsilon_{0} E^{2} $
- $ \frac{1}{2} \varepsilon_{0} E^{2}\,Ad $
- $ \frac{1}{2} \varepsilon_{0} E^{2}\,A/d $
- $ \frac{1}{2} \varepsilon_{0} E^{2}d /A $
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The Correct Option is B
Solution and Explanation
The capacitance of a parallel plate capacitor is
$C=\frac{\varepsilon_{0} A}{d}$
The electric field between the plates is
$E=\frac{V}{d}$
The energy stored in the capacitor is
$U=\frac{1}{2}CV^{2}$
$=\frac{1}{2}\left(\frac{\varepsilon_{0} A}{d}\right)\left(Ed\right)^{2}$
$=\frac{1}{2} \varepsilon_{0}E^{2}Ad$
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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