Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store

What is the average power consumed by a pure capacitor during one cycle of AC?

seo-qna
Last updated date: 22nd Jul 2024
Total views: 348.9k
Views today: 5.48k
Answer
VerifiedVerified
348.9k+ views
Hint: A capacitor is an electrical energy storage system that operates in an electric field. It's a two-terminal passive electronic component.
Capacitance is the term used to describe the effect of a capacitor. Although there is some capacitance between any two electrical conductors in close proximity in a circuit, a capacitor is a device that is specifically engineered to add capacitance to a circuit. Originally, the capacitor was known as a condenser or condenser.

Complete answer:
Average power is the total amount of work or energy converted in a given amount of time. When the meaning makes it obvious, the average power is also clearly referred to as "power." If the time interval Δt reaches zero, the instantaneous power becomes the limiting value of the average power.
The term "alternating current" refers to an electric current that alternates its flow path on a regular basis. One loop occurs as a waveform approaches a full range of positive and negative values.
In an optimal capacitor, the average power expended per cycle is 0.
Based on the instantaneous power supplied to the capacitor, the total power consumed in an optimal capacitor is calculated as follows:
\[{{\text{p}}_{\text{c}}} = {\text{iv}} = \left( {{{\text{i}}_{\text{m}}}\cos \omega {\text{t}}} \right)\left( {{{\text{v}}_{\text{m}}}\sin \omega {\text{t}}} \right)\]
\[{{\text{p}}_{\text{c}}} = {{\text{i}}_{\text{m}}}{{\text{v}}_{\text{m}}}(\cos \omega {\text{t}}\sin \omega {\text{t}})\]
\[{p_c} = \dfrac{{{i_m}{v_m}}}{2}\sin 2\omega t\]
We know that sin \[\omega \]t = 0
Therefore, average power = 0
In relation to direct current (DC), which travels only in one direction, alternating current (AC) is an electric current that regularly reverses direction and varies its amplitude continuously over time. Alternating current is the kind of electricity that is supplied to businesses and homes, and it is the kind of electricity that is used by customers as they plug in kitchen equipment, televisions, fans, and electric lamps to a wall outlet. A flashlight's battery cell is a popular source of DC electricity. When modifying current or voltage, the abbreviations AC and DC are sometimes used to denote simply alternating and direct.

Note: The rate of flow of a charge Q(t) flowing through any part of an electric circuit is known as the current I(t), but real charges – electrons – cannot travel through the dielectric layer of a capacitor. Instead, for any electron that leaves the positive plate, one accumulates on the negative plate, resulting in an electron loss and consequent positive charge on one electrode that is equal to and opposite the cumulative negative charge on the other.