**Chapter 19:** DC Circuits – Giancoli Physics

19.1: EMF and Terminal Voltage

electromotive force (emf)

internal resistance

terminal voltage Vab = Va – Vb

Vab = E – Ir

19.2: Resistors in Series and in Parallel

V = V1 + V2 + v3 = IR1 + IR2 + IR3

V = I * Req

Req = R1 + R2 + R3

19.3: Kirchhoff’s Rules (“laws”)

First some terminology is in order:

There are several **Kirchhoff’s laws**, all named after Gustav Kirchhoff: In electrical engineering – this chapter – we are only concerned with Kirchoff’s circuit laws. Electrical engineers use them so often, that they are called **Kirchhoff’s laws** even thought that is technically incorrect. As you can see here, there are many rules that Kirchoff discovered.

- Kirchhoff’s circuit laws (electrical circuits)
- Kirchhoff’s law of thermal radiation
- Kirchhoff equations (fluid dynamics)
- Kirchhoff’s three laws of spectroscopy
- Kirchhoff’s law of thermochemistry

Secondly, although electrical engineers call these “laws”, these in fact are not “laws” of nature! Rather, they are extremely useful approximations, useful in electrical circuits.

They are true in the sense that they give correct results, for the types of circuits shown in these examples.

If you look at every possible interaction of electricity in the universe, you will find cases where Kirchoff’s rules don’t give the correct result.That’s Ok, they aren’t supposed to. They are just useful approximations: If you want to see the real rules, that always work in every possible case, see Maxwell’s Equations.

Here are Kirchoff’s two rules (“laws”) for electrical circuits:

### An example:

*

### NCEA Level 3 Physics Electricity AS91526 Kirchhoff’s Laws: SlideShare

19.4: EMF’s in Series and in Parallel; Charging a Battery

19.5: Circuits Containing Capacitors in Series and in Parallel

19.6: *RC* Circuits—Resistor and Capacitor in Series

19.7: Electric Hazards

19.8: Ammeters and Voltmeters—Measurement Affects the Quantity Being Measured

- 19.1: EMF and Terminal Voltage (3)
- 19.2: Resistors in Series and in Parallel (10)
- 19.3: Kirchhoff’s Rules (8)
- 19.4: EMF’s in Series and in Parallel; Charging a Battery (1)
- 19.5: Circuits Containing Capacitors in Series and in Parallel (9)
- 19.6:
*RC*Circuits—Resistor and Capacitor in Series (4) - 19.7: Electric Hazards
- 19.8: Ammeters and Voltmeters—Measurement Affects the Quantity Being Measured (8)

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## Thevenin’s Theorem

### Any combination of batteries and resistances with two terminals can be replaced by a single voltage source e and a single series resistor r. The value of e is the open circuit voltage at the terminals, and the value of r is e divided by the current with the terminals short circuited. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/thevenin.html

Animation of Thevenin’s Theorem

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# Limitations of Kirchoff’s laws

### As stated above, Kirchoff’s “laws” are actually useful rules, but they are not absolute laws of nature. Why not? Under what circumstances would they not work?

### On Physics.Stackexchange.Com, an electrical engineering Ph.D. student (“Gotaquestion”) offers us this explanation:

### Kirchhoff’s loop rule is also called Kirchhoff’s voltage law (KVL). Which is different from Kirchhoff’s current rule which is also called Kirchhoff’s current law (KCL).

### KVL is derived from the Maxwell–Faraday equation for a static magnetic field (i.e. the derivative of B with respect to time is zero).

### KCL is derived from charge continuity equation which is equation 3 here:

Faraday’s Law and Electromagnetic Induction, and Electromagnetic Energy and Power Flow

### A well known case in which KVL doesn’t apply is when having a varying magnetic field enclosed by the circuit being studied. The presence of time varying magnetic field makes the measured voltage non-unique (depends on the branch used to measure the voltage). Have a look at page 3 of this presentation. https://courses.cit.cornell.edu/ece303/Lectures/lecture11.pdf

### A well known case in which KCL is limited is when having a voltage source with very high frequency such that effects like parasitic capacitance can no longer be ignored. In those cases wires (or conductors) are treated as transmission lines. In such a case a current can flow even in an open circuit.

### Can Kirchhoff laws be applied to any circuit?

An even more detailed explanation of the limits of these rules is presented by John Denker. Most of his materials were written to answer questions that came up on Phys-L, the Forum for Physics Educators.

Kirchhoff’s Circuit “Laws” by John Denker

## Learning Standards

**Massachusetts 2016 Science and Technology/Engineering (STE) Standards**

HS-PS2-9(MA). Evaluate simple series and parallel circuits to predict changes to voltage, current, or resistance when simple changes are made to a circuit

HS-PS3-1. Use algebraic expressions and the principle of energy conservation to calculate the change in energy of one component of a system… Identify any transformations from one form of energy to another, including thermal, kinetic, gravitational, magnetic, or electrical energy. {voltage drops shown as an analogy to water pressure drops.}

HS-PS3-2. Develop and use a model to illustrate that energy at the macroscopic scale can be accounted for as either motions of particles and objects or energy stored in fields [e.g. electric fields.]

HS-PS3-3. Design and evaluate a device that works within given constraints to convert one form of energy into another form of energy.{e.g. chemical energy in battery used to create KE of electrons flowing in a circuit, used to create light and heat from a bulb, or charging a capacitor.}