chapter 27: circuits introduction what are we going to talk about in chapter 28: what is an...

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Chapter 27: Circuits Introduction What are we going to talk about in chapter 28: What is an electromotive force (E: emf)? What is the work done by an emf? What is an ideal emf? How does it differ from real emfs? What is Kirchhoff’s voltage law (KVL)? What is Kirchhoff’s current law (KCL)? Resistors connected: series and/ or parallel

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Page 1: Chapter 27: Circuits Introduction What are we going to talk about in chapter 28: What is an electromotive force ( E : emf)? What is the work done by an

Chapter 27: Circuits

Introduction

What are we going to talk about in chapter 28:

• What is an electromotive force (E: emf)?

• What is the work done by an emf?

• What is an ideal emf? How does it differ from real emfs?

• What is Kirchhoff’s voltage law (KVL)?

• What is Kirchhoff’s current law (KCL)?

• Resistors connected: series and/ or parallel

• RC circuits, time constant: = R C

Page 2: Chapter 27: Circuits Introduction What are we going to talk about in chapter 28: What is an electromotive force ( E : emf)? What is the work done by an

An emf (ElectroMotive Force) device is a [charge pump] device that (unlike a capacitor) maintains a constant potential difference between a pair of terminals.

Emfs do work on charges.

27-2: Pumping charges

Examples: batteries, generators and solar cells.

Page 3: Chapter 27: Circuits Introduction What are we going to talk about in chapter 28: What is an electromotive force ( E : emf)? What is the work done by an

27-3: Work, energy and emf

There must be a source of energy in the emf device that moves positive charge carriers from the negative (low potential and potential energy) terminal to the positive (high potential and potential energy) terminal. This source may be chemical, mechanical, thermal or electromagnetic in nature.

The internal chemistry causes a net flow of positive charge carriers from the negative terminal to the positive terminal (i.e. in the direction of the emf arrow).

Page 4: Chapter 27: Circuits Introduction What are we going to talk about in chapter 28: What is an electromotive force ( E : emf)? What is the work done by an

The emf (E) of a device is the work per unit charge that the device does in moving charge from its LP terminal to its HP terminal.

E = dW/dq

[E] = volt

What is an ideal emf?

How does it differ from real emfs?

As an example for emfs and their function, let’s look at figure 28-2.

Page 5: Chapter 27: Circuits Introduction What are we going to talk about in chapter 28: What is an electromotive force ( E : emf)? What is the work done by an

We can analyze using the energy method:

dW = E dq = E i dt == i2 R dt

i = E /R

27-4:Calculating the current in a single-loop circuit:

Page 6: Chapter 27: Circuits Introduction What are we going to talk about in chapter 28: What is an electromotive force ( E : emf)? What is the work done by an

We can analyze using the potential method: Using Kirchhoff’s voltage law.

KVL: The algebraic sum of the changes in potential encountered in a complete traversal of any loop of a circuit must be zero.

i = E /R

Page 7: Chapter 27: Circuits Introduction What are we going to talk about in chapter 28: What is an electromotive force ( E : emf)? What is the work done by an

Note:

What happens when you cross a resistor in the same (or opposite) direction as the current? [resistance rule]

What happens when you cross an emf in the same (or opposite) direction as the current? [emf rule]

Checkpoint 1

Page 8: Chapter 27: Circuits Introduction What are we going to talk about in chapter 28: What is an electromotive force ( E : emf)? What is the work done by an

Internal resistance: In the case of a real battery, there is internal resistance.

E – i r - i R = 0

There is a difference, for real batteries, between emf and terminal voltage.

27-5 :Other single loop circuits:

Page 9: Chapter 27: Circuits Introduction What are we going to talk about in chapter 28: What is an electromotive force ( E : emf)? What is the work done by an

Resistance in series:

Req = Ri

Resistances connected in series can be replaced with an equivalent resistance that has the same current and the same total potential difference as the actual resistances.

Checkpoint 2

Page 10: Chapter 27: Circuits Introduction What are we going to talk about in chapter 28: What is an electromotive force ( E : emf)? What is the work done by an

27-6: Potential differences:

To find the potential difference between two points, apply resistance rule and emf rule in going from one point to the other.

Page 11: Chapter 27: Circuits Introduction What are we going to talk about in chapter 28: What is an electromotive force ( E : emf)? What is the work done by an

When the battery is in “normal” mode:

P = Pemf – Pr

When the battery is recharging:

P = Pemf + Pr

Checkpoint 3

P = i V

Pemf = i E

Pr = i2 r

Power, potential and emf:

Page 12: Chapter 27: Circuits Introduction What are we going to talk about in chapter 28: What is an electromotive force ( E : emf)? What is the work done by an

Resistance in parallel:

(Req)-1 = (Ri)-1

Resistances connected in parallel can be replaced with an equivalent resistance that has the same potential difference and the same total current as the actual resistances.

27-7: Multi-loop circuits:

Kirchhoff’s current law (KCL): iin = iout

For two resistances in parallel:

Req = R1 R2 /(R1 + R2)

Checkpoint 4

Page 13: Chapter 27: Circuits Introduction What are we going to talk about in chapter 28: What is an electromotive force ( E : emf)? What is the work done by an

You need to solve a “differential equation” to find how the charge and current change with time.

27-9: RC circuits:

Charging an RC circuit:

= R C

Io = E /R

Q = E C

q(t) = Q (1-e-t/])

I(t) = Io exp-t/

Page 14: Chapter 27: Circuits Introduction What are we going to talk about in chapter 28: What is an electromotive force ( E : emf)? What is the work done by an

Discharging an RC circuit:

q(t) = Q exp-t/

I(t) = Io exp-t/