Chapter%2027.%20Circuits

1
Chapter 27. Circuits

• 27.1. What is Physics?      
• 27.2. "Pumping" Charges      
• 27.3. Work, Energy, and Emf      
• 27.4. Calculating the Current in a Single-Loop
  Circuit      
• 27.5. Other Single-Loop Circuits     
• 27.6. Potential Difference Between Two
  Points      
• 27.7. Multiloop Circuits      
• 27.8. The Ammeter and the Voltmeter      

2
What is Physics?  

• How can you maintain charges to flow?

3
Pumping Charges

• To produce a steady flow of charge, you need a
  charge pump (battery), a device thatby doing
  work on the charge carriersmaintains a potential
  difference between a pair of terminals. We call
  such a device an emf device, and the device is
  said to provide an emf e , which means that it
  does work on charge carriers.
• The maximum potential difference between the
  terminals of the battery is called the
  electromotive force (emf) e of the battery

4
Work, Energy, and Emf

• Within the emf device, positive charge carriers
  move from a region of low electric potential and
  thus low electric potential energy. This motion
  is just the opposite of what the electric field
  between the terminals would cause the charge
  carriers to do.
• there must be some source of energy within the
  device, enabling it to do work on the charges by
  forcing them to move as they do. The energy
  source may be chemical, as in a battery or a fuel
  cell. It may involve mechanical forces, as in an
  electric generator
• Emf is

                                                                                                

5
emf device

• An ideal emf device is one that lacks any
  internal resistance to the internal movement of
  charge from terminal to terminal. The potential
  difference between the terminals of an ideal emf
  device is equal to the emf of the device.

                                                                                                

• A real emf device, such as any real battery, has
  internal resistance to the internal movement of
  charge. When a real emf device is not connected
  to a circuit, and thus does not have current
  through it, the potential difference between its
  terminals is equal to its emf. However, when that
  device has current through it, the potential
  difference between its terminals differs from its
  emf.

6

• If the current flows from the negative terminal
  to the positive terminal of the emf device, the
  other types of energy will be converted to
  electrical energy in the circuit
• If the current flows from the positive terminal
  to the negative terminal of the emf device,
  electrical energy in the circuit will be stored
  in the emf device as other types of energy.

7
Calculating the Current in a Single-Loop Circuit


                                                                                                

• LOOP RULE The algebraic sum of the changes in
  potential encountered in a complete traversal of
  any loop of a circuit must be zero.
• RESISTANCE RULE For a move through a resistance
  in the direction of the current, the change in
  potential is -iR in the opposite direction it is
  iR.
• EMF RULE For a move through an ideal emf device
  in the direction of the emf arrow, the change in
  potential is e in the opposite direction it is
  -e.

8
 Checkpoint

• The figure shows the current i in a single-loop
  circuit with a battery B and a resistance R (and
  wires of negligible resistance), (a) Should the
  emf arrow at B be drawn pointing leftward or
  rightward? At points a, b, and c, rank (b) the
  magnitude of the current, (c) the electric
  potential, and (d) the electric potential energy
  of the charge carriers, greatest first.

    

                                                                                           
9
Internal Resistance
10
Resistances in Series

• The same electric current through each device.
• The sum of the potential differences across the
  resistances is equal to the applied potential
  difference V. VV1V2V3.
• Resistances connected in series can be replaced
  with an equivalent resistance Req that has the
  same current i and the same total potential
  difference V as the actual resistances.

                                                                                              

11
Example  Resistors in a Series Circuit

• A 6.00-W resistor and a 3.00-W resistor are
  connected in series with a 12.0-V battery, as
  Figure 20.16 indicates. Assuming that the battery
  contributes no resistance to the circuit, find
  (a) the current, (b) the power dissipated in each
  resistor, and (c) the total power delivered to
  the resistors by the battery.

12
Resistances in Parallel

• The same voltage is applied across each device
• ii1i2
• The equivalent resistance is

13
Question

• In one of the circuits in the drawing,
  none of the resistors is in series or in
  parallel. Which is it? Explain.

14
Example 7

• A 47.0 W and a 33.0 W resistor are connected
  in parallel. What is the equivalent resistance of
  the resistors? How much current would a 12.0 V
  battery supply to the network and how much
  current would flow through each resistor?

15
Potential Difference Between Two Points


                                                                                  

• To find the potential between any two points in
  a circuit, start at one point and traverse the
  circuit to the other point, following any path,
  and add algebraically the changes in potential
  you encounter.

The terminal-to-terminal potential difference V
across the real battery is different from e.
16
Sample Problem

• The emfs and resistances in the circuit of Fig.
  27-8 a have the following values

                                                                                                                                                                                        


                                                                                                                                                                                                               

1. What is the current i in the circuit?
2. b) What is the potential difference between the
   terminals of battery 1 in Fig. 27-8 a?

    

17
Grounding a Circuit


                                                                                  
18
Power, Potential, and Emf
The energy transfer from the emf device to the
outside charge carriers is
19
Multiloop Circuits
                                                                                              

• KIRCHHOFFS RULES
• Junction rule. The sum of the magnitudes of the
  currents directed into a junction equals the sum
  of the magnitudes of the currents directed out of
  the junction.
• Loop rule. Around any closed-circuit loop, the
  sum of the potential drops equals the sum of the
  potential rises.

20
Sample Problem
Figure 27-11 a shows a multiloop circuit
containing one ideal battery and four resistances
with the following values



                                                                                                                                                                                                              

• (a) What is the current through the battery?
• (b) What is the current i2 through R2?

                                                                                                                                                                                  
21
Sample Problem
Figure 27-12 shows a circuit whose elements have
the following values


                                                                                                                                       

                                                                                      

• What are the magnitude and direction of the
  current in each of the three branches?

22
The Ammeter and the Voltmeter


                                                                                          
23
Conceptual Questions

1. The power rating of a 1000-W heater specifies the
   power consumed when the heater is connected to an
   ac voltage of 120 V. Explain why the power
   consumed by two of these heaters connected in
   series with a voltage of 120 V is not 2000 W.
2. A number of light bulbs are to be connected to a
   single electrical outlet. Will the bulbs provide
   more brightness if they are connected in series
   or in parallel? Why?