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# DC circuits AP

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.

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:

*

### 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 25.18 Simple circuit with an external resistor R and a 12 Volt source with an internal resistance r.

• 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)

DC circuits Giancoli Chap 19

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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

### 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.}