MCAT Physics and Math Review
Chapter 6: Circuits
Batteries, electric circuits, and electrical equipment pervade our everyday world. Think of any piece of equipment, tool, or toy that has a battery or a power cord, and you’ve identified an object that depends on the movement of electrons and the delivery of electrical potential energy to carry out its function. Turn on a light, watch TV, or toast bread, and you can literally watch electrons at work as they emit light. Electricity is not restricted to the inorganic, material world—even in our bodies, we find electricity serving a key role in a number of physiological functions. Not only do the neurons in our brain and conduction system in our heart rely on electricity, but so does every cell that utilizes mitochondria to carry out oxidative phosphorylation.
This chapter reviews the essentials of circuits. From this broad knowledge base, we will draw on specific topics within circuit theory: conductivity, electromotive force (emf), resistance, power, Kirchhoff’s laws, resistors, capacitors, meters, and series and parallel arrangements of circuit components. As you encounter the concepts of this chapter and the equations associated with them, remember this: the MCAT approaches the topic of circuits with a greater emphasis on the concepts than on the math. You will be expected to calculate, say, the equivalent resistance for resistors in series or parallel, but the circuits you encounter on Test Day will, on the whole, be simpler than what you may have seen in your college physics class.
In the last chapter we examined the behaviors of still charges, but in most cases we are interested in the movement of charge, or current. Because of historical conventions, current is considered the flow of positive charge—even though only negative charges are actually moving. Any conductive substance may act as a medium through which current can pass.
Conductivity can be divided into two categories: metallic conductivity, as seen in solid metals and the molten forms of some salts, or electrolytic conductivity, as seen in solutions. Conductance is the reciprocal of resistance, a property we will examine in detail later. The SI unit for conductance is the siemens (S), sometimes given as siemens per meter for conductivity.
Some materials allow free flow of electric charge within them; these materials are called electrical conductors. Metal atoms can easily lose one or more of their outer electrons, which are then free to move around in the larger collection of metal atoms. This makes most metals good electrical and thermal conductors. The metallic bond has often been visualized as a sea of electrons flowing over and past a rigid lattice of metal cations. While this model is generally appropriate for the MCAT, metallic bonding is more accurately descried as an equal distribution of the charge density of free electrons across all of the neutral atoms within the metallic mass.
Remember that the metals are found on the left side of the Periodic Table. These are the atoms with the lowest ionization energies; thus, it is easiest for these atoms to lose electrons. Due to this weak hold, electrons are free to move around in the metal, conducting electrical charges. Periodic trends are discussed in Chapter 2 of MCAT General Chemistry Review.
While not substantially different from metallic conductivity, it is important to note that electrolytic conductivity depends on the strength of a solution. Distilled deionized water has such a low ion concentration that it may be considered an insulator, while sea water and orange juice are excellent conductors. Conductivity in an electrolyte solution is measured by placing the solution as a resistor in a circuit and measuring changes in voltage across the solution. Because concentration and conductivity are directly related, this method is often used to determine ionic concentrations in solutions, such as blood. One caveat is that conductivity in nonionic solutions is always lower than in ionic solutions. While the concentration of total dissolved solids does relate to conductivity, the contribution of nonionic solids is much, much less important than ion concentration.
Chapter 5 of MCAT Physics and Math Review introduced the concept of electrical current: the flow of charge between two points at different electrical potentials connected by a conductor, such as a copper wire. The magnitude of the current I is the amount of charge Q passing through the conductor per unit time ∆t, and it can be calculated as:
The SI unit of current is the ampère . Charge is transmitted by a flow of electrons in a conductor, and because electrons are negatively charged, they move from a point of lower electrical potential to a point of higher electrical potential (and, in doing so, reduce their electrical potential energy). By convention, however, the direction of current is the direction in which positive charge would flow (from higher potential to lower potential). Thus, the direction of current is opposite to the direction of actual electron flow. The two patterns of current flow are direct current (DC), in which the charge flows in one direction only, and alternating current (AC), in which the flow changes direction periodically. Direct current is produced by household batteries, while the current supplied over long distances to homes and other buildings is alternating current. Our discussion of circuits will assume direct current, which is tested on the MCAT to the exclusion of alternating current.
A potential difference (voltage) can be produced by an electrical generator, a galvanic (voltaic) cell, a group of cells wired into a battery, or—as seen in classic science fair projects—even a potato. When no charge is moving between the two terminals of a cell that are at different potential values, the voltage is called the electromotive force (emf or ε). Do not be misled by this term, as emf is not actually a force; it is a potential difference (voltage) and, as such, has units of joules per coulomb —not newtons. It may be helpful to think of emf as a “pressure to move” that results in current, in much the same way that a pressure difference between two points in a fluid-filled tube causes the fluid to flow.
The standard batteries in flashlights and remote controls are examples of galvanic (voltaic) cells. These house spontaneous oxidation–reduction reactions that generate emf as a result of differences in the reduction potentials of two electrodes. Electrochemistry is discussed in Chapter 12 of MCAT General Chemistry Review.
Currents (and circuits in general) are governed by the laws of conservation. Charge and energy must be fully accounted for at all times and can be neither created nor destroyed. An electric circuit is a conducting path that usually has one or more voltage sources (such as a battery) connected to one or more passive circuit elements (such as resistors). Kirchhoff’s laws are two rules that deal with the conservation of charge and energy within a circuit.
Kirchhoff’s Junction Rule
At any point or junction in a circuit, the sum of currents directed into that point equals the sum of currents directed away from that point. This is an expression of conservation of electrical charge and can be expressed as
Iinto junction = Ileaving junction
Kirchhoff’s junction rule is just like a fork in a river. There are a certain number of water molecules in a river, and at any junction, that number has to go in one of the diverging directions; no water molecules spontaneously appear or disappear. The same holds true for the amount of current at any junction.
Three wires (a, b, and c) meet at a junction point P, as shown below. A current of 5 A flows into P along wire a, and a current of 3 A flows away from P along wire b. What is the magnitude and direction of the current along wire c?
The sum of currents entering P must equal the sum of the currents leaving P. Assume for now that Ic flows out of P. If we find that it is negative, then we know the current must be going the other direction (into P).
Thus, a current of 2 A flows out of P along wire c.
Kirchhoff’s Loop Rule
Around any closed circuit loop, the sum of voltage sources will always be equal to the sum of voltage (potential) drops. This is a consequence of the conservation of energy. All the electrical energy supplied by a source gets fully used up by the other elements within that loop. No excess energy appears, and no energy disappears that cannot be accounted for. Of course, energy can be changed from one form to another, so the kinetic energy of the electrons can be converted to thermal energy, light, or sound by the particular apparatus that is connected into the circuit. Remember that although Kirchhoff’s loop rule is a consequence of the law of conservation of energy, this law is in terms of voltage (joules per coulomb), not just energy (joules). This can be expressed mathematically as
Vsource = Vdrop
If all of the voltage wasn’t “used up” in each loop of the circuit, then the voltage would build after each trip around the circuit, which is impossible.
MCAT Concept Check 6.1:
Before you move on, assess your understanding of the material with these questions.
1. Define the following terms and provide their SI units.
· Electromotive force (emf):
2. Which likely has a higher conductivity: 1 M glucose or 0.25 M NaCl? Why?
3. True or False: In a circuit, the number of electrons entering a point and leaving that point are the same.
4. True or False: The sum of the voltage sources in a circuit is equal to the sum of the voltage drops in that circuit.