Circuits – Capacitors, Part 1 | MCAT Physics Prep

Need help preparing for the MCAT physics section? MedSchoolCoach expert, Ken Tao, will teach you Part 1 of what you need to know about capacitors within circuits. Watch this video to learn how to do well on the physics section of the MCAT exam!

A capacitor is a circuit element that consists of two parallel conducting plates separated by either a vacuum or an insulating material called a dielectric. Capacitors are capable of storing charge, one plate capable of storing positive charge and one plate capable of storing negative charge. The circuit element for capacitors on a circuit diagram is two parallel lines of the same length. The equation for the amount of charge that can be stored on a capacitor is below, where Q is charge, C is capacitance, and V is voltage across the capacitor. There is voltage across the capacitor because one plate can store positive charge and the other plate can store negative charge, creating a potential difference. The equation below tells us that a capacitor with higher capacitance will be able to store more charge if it is held at a greater voltage.

A capacitor is capable of storing voltage which can be used to produce an electrical current. Therefore, a charged capacitor can serve the same function as a battery. The calculation for the potential energy stored in a capacitor, PE = ½QV, is shown below. The equation can be re-arranged to be understood in terms of capacitance by substituting in the equation Q = CV. The various rearrangements of the equation for capacitor potential energy are shown below.

Capacitance

Capacitance describes how much charge can be stored on a capacitor for a given voltage. In the equation Q = CV, it functions like a constant for a given capacitor, because the more charge stored on the two plates, the greater the voltage. The capacitance of a capacitor depends on several properties described by the equation below. A is the area of one of the parallel plates, and d is the distance between the plates. κ is the dielectric constant, which is a multiplier for capacitance that changes based on the insulating material between the two plates. For capacitors with a dielectric that is not a vacuum, you will be given a value for kappa. For a vacuum, the value of κ is 1. ε₀ is a constant describing permittivity of free space, which you do not need to know for the MCAT.

Capacitors in a Circuit

How are capacitors able to store charge in a circuit. If a capacitor is connected to a battery, it has some capacitance (C) due to the battery supplying some voltage. When a capacitor has not yet been filled with charges, Q = 0. Therefore, before a circuit has run and the plates have filled with charges, the charge on the capacitor is zero. When we turn a battery on, electrons are going to leave the negative terminal of the battery and move around the circuit until they reach the bottom plate of the capacitor. As electrons accumulate on the bottom plate of a capacitor, they will repel electrons on the top plate of the capacitor, allowing for the build-up of positive charge on the top plate. As the bottom plate and top plate accumulate opposite charges, they will build up a potential difference of voltage. This accumulation will continue until the voltage on the capacitor is equal to the voltage of the battery, at which point we say that the capacitor is fully charged. The maximum charge on the capacitor at this point can be calculated by multiplying the capacitance of the capacitor by the voltage of the battery/capacitor.

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