chapter 21 electric current and direct- current...

Chapter 21

Electric Current and Direct-Current Circuits

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Overview of Chapter 21

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• Electric Current and Resistance

• Energy and Power in Electric Circuits

• Resistors in Series and Parallel

• Kirchhoff’s Rules

• Circuits Containing Capacitors

• RC Circuits

21-1 Electric Current

Electric current is the flow of electric charge from one place to another.

Electric circuit: A closed path through which charge can flow, returning to its starting point.

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21-1 Electric Current

• Battery has a potential difference between terminals

• Chemical reactions separate electrons from atoms…

• Analogy…

- Current to flows through the flashlight bulb similar to someone lifting water which flows through the paddle wheel….

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21-1 Electric Current

A battery that is disconnected from any circuit has an electric potential difference between its terminals called the electromotive force (emf)

Remember – despite its name, the emf is an electric potential, not a force. Amount of work it takes to move a charge ΔQ from one terminal to the other is:

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21-1 Electric Current

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• Current flows from the positive terminal to the negative

• Decided before it was realized that electrons are negatively charged.

• The electrons move the other way…

21-1 Electric Current

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Actual motion of electrons along a wire is quite slow…

• Electrons spend most of their time bouncing around randomly with small velocity component

- Opposite to the direction of the current.

• The electric signal propagates much more quickly…

21-2 Resistance and Ohm’s Law

Wires present some resistance to the motion of electrons. Ohm’s law relates the voltage to the current:

Be careful – Ohm’s law is not a universal law and is only useful for certain materials (which include most metallic conductors).

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21-2 Resistance and Ohm’s Law

Solving for the resistance, we find:

The units of resistance, volts per ampere, are called ohms:

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21-2 Resistance and Ohm’s Law

• Two wires of the same length and diameter will have different resistances if they are made of different materials.

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• Property of a material is called the resistivity.

21-2 Resistance and Ohm’s Law

The difference between insulators, semiconductors, is quantified by resistivity..

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21-2 Resistance and Ohm’s Law

In general.. •Resistance of materials goes up as the temperature goes up, due to thermal effects. This property can be used in thermometers. •Resistivity decreases as the temperature decreases…

Class of materials called superconductors

•Resistivity drops suddenly to zero at a finite temperature, called the critical temperature TC….

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21-2 Resistance and Ohm’s Law

Superconductors in action. The ATLAS experiment at the LHC. MRI machines.

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21-3 Energy and Power in Electric CircuitsWhen a charge moves across a potential difference, its potential energy changes:

Therefore, the power it takes to do this is

Remember…

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21-3 Energy and Power in Electric CircuitsIn materials for which Ohm’s law holds, the power can also be written:

This power mostly dissipates as heat inside a resistive material…

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21-3 Energy and Power in Electric Circuits

When the electric company sends you a bill, your usage is quoted in kilowatt-hours (kWh). They are charging you for energy use, and kWh are a measure of energy.

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21-4 Resistors in Series and Parallel

Resistors connected end to end are said to be in series. They can be replaced by a single equivalent resistance without changing the current in the circuit.

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21-4 Resistors in Series and Parallel

Relation due to current through the series resistors being the same for each..

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21-4 Resistors in Series and Parallel

•Resistors are in parallel when they are across the same potential difference…

•They can again be replaced by a single equivalent resistance..

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21-4 Resistors in Series and Parallel

Relation due to potential difference across parallel resistors being the same for each..

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21-4 Resistors in Series and ParallelIf a circuit is more complex:

•Start with combinations of resistors that are either purely in series or in parallel.

•Replace these with their equivalent resistances; as you go on you will be able to replace more and more of them.

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21-5 Kirchhoff’s Rules• Even more complex circuits cannot be broken down into series

and parallel pieces.

• Kirchhoff’s rules are needed.

• The junction rule is a consequence of charge conservation; the loop rule is a consequence of energy conservation.

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21-5 Kirchhoff’s Rules

The junction rule: At any junction, the current entering the junction must equal the current leaving it.

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21-5 Kirchhoff’s Rules

The loop rule: The algebraic sum of the potential differences around a closed loop must be zero (it must return to its original value at the original point).

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21-5 Kirchhoff’s Rules

Using Kirchhoff’s rules:

•The variables for which you are solving are the currents through the resistors.

•You need as many independent equations as you have variables to solve for.

•You will need both loop and junction rules.

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21-6 Circuits Containing Capacitors

Capacitors can also be connected in series or in parallel.

When capacitors are connected in parallel, the potential difference across each one is the same.

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21-6 Circuits Containing Capacitors

Therefore, the equivalent capacitance is the sum of the individual capacitances:

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21-6 Circuits Containing Capacitors

•Capacitors connected in series do not have the same potential difference across them.

•They do all carry the same charge.

•The total potential difference is the sum of the potential differences across each one.

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21-6 Circuits Containing Capacitors

Therefore, the equivalent capacitance is

Capacitors in series combine like resistors in parallel, and vice versa.

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21-7 RC Circuits

Circuit containing only batteries and capacitors

• Charge appears almost instantaneously on the capacitors when the circuit is connected.

If the circuit contains resistors as well…

•Not the case… •Known as a RC circuit

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21-7 RC Circuits

It can be shown that the charge on the capacitor increases as:

Here, τ is the time constant of the circuit:

And is the final charge on the capacitor, Q.

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21-7 RC CircuitsHere is the charge vs. time for an RC circuit:

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21-7 RC Circuits

It can be shown that the current in the circuit has a related behavior:

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Answer: a) 14 CAnswer: b) 8.8 x 1019 electrons

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Hint: Resistivity of silver is 1.59 x 10-8 Ω⋅m

Answer: 0.5 Ω

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Answer: 33 Ω

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Note on Kirchoff’s laws…

•Loop rule: -Sum of the potential differences around a closed loop must be zero

•What does this mean?

-EMF adds a potential difference to current -Resistors take it away

+-

R1

R2

R3

ε = +15 V

I

ε + V1+V2+V3 = 0

ε -IR1-IR2-IR3 = 0

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Note on Kirchoff’s laws…

+-

R1

R2

ε1

εT

I

ε -IR1-IR2+ε1 = 0

+-

+-

R1

R2

εT

I

ε2 +-

ε -IR1-IR2-ε2 = 0

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Answer: 0.889 A

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Answer: 6.1 kΩ

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