Download unit 3 worksheet 1

EM Unit 3 – Objectives
What you should know when all is said and done.
By the time you finish all labs, worksheets and related activities, you should be able to:
1. Use the electric field model developed in earlier units to describe charge flow in a conductor.
2. Define current as "charge flow rate" or quantity of charge per unit time passing a cross-sectional
area in the conductor.
 Distinguish between "flow rate" and "drift velocity."
 By use of examples and activities, define and apply equation I = ∆q/∆t
 Use the ammeter as a device to measure flow rate.
3. Develop a quantitative model for resistance in ohmic materials, and qualitatively describe
reasons for deviations from this behavior (e.g. thermal motion of atoms causing temperaturedependence on resistance).
 Use ammeter and voltmeter measurements to develop Ohm's Law.
 Use light bulbs to show an example of a non-ohmic system ( V proportional to I2).
4. Develop a qualitative microscopic model for resistance, with flow of charge carriers hindered by
other material components (vibrating atoms & other charge carriers).
5. For simple series and parallel circuit arrangements, discover and explain the relationships
among:
 Applied voltage and voltage drops across resistors.
 Total current and currents in each branch of a circuit.
 Total equivalent resistance and resistance of the resistors in series and parallel.
 Power dissipated by a resistor and the voltage drop and current.
6. Predict the effect of an addition (or removal) of an element in an existing circuit.
Theoretical Background of Surface Charge Distribution for Resistive Wires with Currents
In electronic applications one usually treats a wire as a perfect conductor in which there is no
electric field or potential drop. If that were the case, there would be no need for an electric field to
maintain current. If we are to correctly represent the situation then we must really treat the entire
length of wire as a resistive substance which does contain a small electric field and a small potential
drop. A resistive substance provides a force against the electron current which actually depends on
the drift velocity itself. The current of a wire is proportional to the drift velocity. Therefore, for a
desired current there will be a specific resistive force which must matched in order for the current to
flow at a constant rate. In order to match this resistive force we must produce an electric field in the
wire. The electric field within a wire is caused by a non-uniform distribution of surface charge. As a
model, consider the simplified case of rings of charge along a wire shown in figure 1a, 1b, and 1c.
Each of these arrangements produces an equal net electric field to the right (that is an equal force on
a test charge placed in the field.) We see that the electrical field within a wire is independent of the
sign of the charges but dependent upon the change in charge density.
It is this difference in charge density that leads to a continuous electrical field in a wire as shown
below in figure 2.
Figure 2
Making A Relative Charge Density Map:
A relative charge density map is another method for describing characteristics of the charge distribution
in a circuit. This method graphically depicts relative increases in surface charge density. When creating a
charge density map, use the following conventions:
1. The relative charge density will be graphically depicted at increments around a circuit.
2. Assign the negative terminal of the battery to be 0 Volts, and represent this with a short line.
3. Using a voltmeter or calculations, move along the circuit toward the positive terminal and determine
any points where the electric potential increases.
4. Numerically label voltages at the points where the wires meet circuit elements.
5. At the points in the circuit where the electrical potential is found to increase (which corresponds to
points where charge density increases), graphically represent the increase of Charge Density by
increasing the length of the density lines.
6. In a closed circuit, along wires where there is little potential difference (often to small to measure
with a volt meter) there is also little variation in the charge density and the electric field must also be
comparably small for a given length of wire.
7. For simplicity, treat the resistors as very resistive so that they are neutral in surface charge density.
Even though this implies that there will be no gradient of the charge density on the resistor itself the
greatest electric field and potential drop is there in the resistors. This is because the electric field there
is really due to the different charge density across the resistor. The charge density is different in the
wire at one end of the resistor than it is in the wire at the other end.
EM Unit 3 Review
1. An uneven distribution of charge produces an electric field; this can be deduced by a difference in
electric potential (∆V). If there is a conducting pathway between the areas of uneven charge
distribution, the field will drive charge until the distribution is uniform.
2. The greater the resistance in the conducting path, the longer it will take for the charge to re-distribute
itself. Thus, it takes longer for a capacitor to discharge through along bulb than through a round one.
(WS 1)
3. A battery maintains a difference in electric potential by means of chemical reactions that transfer
chemical potential energy to electric potential energy.
Using the Franklin convention, the battery raises the
+ terminal = higher electric potential
potential of + charges which flow through a circuit
and return to zero potential when they reach the
negative terminal.
- terminal = lower electric potential
4. While the drift velocity of individual charges in a wire is on the order of a millimeter/second, the electric
field propagates through a circuit at the speed of light. Thus, charge begins to flow everywhere in a
circuit the instant a conducting pathway is made between regions of uneven charge density.
5. Flow rate of charge (current) is a measure of how much charge moves past a given position in a time
interval (C/s or amperes). It is not the same as drift velocity
3V
b
a
6. In a wire (minimal resistance), the potential difference is very
small (weak field) and the charges drift slowly. Through a
resistor, where the potential difference is large (strong E field),
12 
the drift velocity must be greater to achieve the same overall flow
rate of charge.
Q: Where in the circuit at right are the charges moving most
6
rapidly?
c
d
7. The power dissipated in a resistive element (bulb or resistor) is a
function of both the potential drop and the current. P  I  V The unit of power is the watt.
J C J
W  
s s C
8. For a given resistance, the potential is proportional to the current V  R I . This is known as Ohm’s
Law. Rearrangement of this equation and substitution into equation in #7 gives other useful variations
of the power equation.
9. In series circuits, the current is the same everywhere (charge is conserved). Thus, the potential drop
across each resistor is proportional to the resistance. The overall resistance is found by summing the
individual resistance of the resistors: R s  R 1  R 2  R 3  K . Thus, in series circuit problems, you
should first find the equivalent resistance of the circuit, then the overall current, then the potential drop
across each resistor.
10. In parallel circuits, the potential drop in each branch is the same. The overall resistance
decreases as the number of branches increases (more paths). The current in each branch is
inversely proportional to the resistance. The equivalent resistance can be found by
1
1
1
1



 K . Thus, in parallel circuit problems, you should first find the
R
R
R
R
p
1
2
3
equivalent resistance, then the overall current, then the current through each branch.
11. In circuits containing resistors in both series and parallel arrangements, use the equivalent
resistance equations to simplify the circuits until they behave as if they had one resistor. Then
find the overall current, and work from there.
UNIT 3 WORKSHEET 1
1. Below is a drawing of two charged plates, one positive and one negative (neglect gravity).
a. Draw the electric field lines.
b. Place a negative charge in the middle of the field. Draw a force diagram for the electron. In
which direction will the charge move when released in the field? Why?
Positiv e
Pla te
Nega tive
Pla te
2. A charged capacitor has two wires connected to it as shown below.
A student uses a voltmeter to measure potential difference between
parts of the setup, and obtains the following data:
Segment
A-B
B-C
C-D
D-A
V (Volts)
+5.0
0
-5.0
0
a. On the diagram below, draw a representation of a) the fields and b) the charge distribution that
gave rise to those fields.
b. On the axes below, sketch a qualitative bar graph of electric field strength as a function of
position. Remember: we're assuming a change in potential indicates the existence of a uniform
field between the two points.
c. On the axes below, construct a quantitative graph of electric potential (not change in electric
potential) as a function of position. Assume the potential at point A is zero.
d. The capacitor is discharged three times. First, it is discharged through a bulb that lights dimly,
then through a bulb that lights very brightly, and finally, without a bulb in the setup. The V
from C to D vs. time for all three discharges is shown below.
i. Which line represents the discharging with no bulb in the setup? How do you know?
ii. Which line represents discharging through the bright bulb? Explain.
EM Unit 3 - Worksheet 2
1. The following graphs represent data collected for three resistors.
V
10
A
B
V
10
5
5
5
C
V
10
2 I
2 I
2 I
a. Which graph(s) represent "ohmic" resistors? Explain.
b. What potential difference exists across resistor A when 1.0 amps flow through it?
c. What is the resistance (in ohms) of resistor B?
In the problems that follow, each cell in a battery provides a potential difference of 1.5 V.
2. In each of the circuits below, all the bulbs are identical. Write what you would expect the
voltage drop across each bulb to be.
B
A
C
3. In each of the diagrams below, consider the part of the circuit in the dashed box.
X
A
L
Y
Z
B
C
L
R
L
A = entering the bulb
B = through the bulb
C = leaving the bulb
X = entering the junction
Y = to R bulb from junction
Z = to L bulb from junction
a. How do the flow rates in A, B and C compare to each other?
b. How does the potential at A, B and C compare to each other? Explain.
c. How do the flow rates in X, Y and Z compare to each other?
d. How does the potential at X, Y and Z compare to each other? Explain.
4. In the circuit below all the bulbs have identical resistance. What is the voltage drop across each
bulb? Sketch the charge density in each of the wires.
B
A
C
5. In the circuit above, how does the flow rate through A compare to that through B? How many times
brighter should A be compared to B? Explain.
6. Consider the series circuit at right.
a
3V
b
a. What is the ∆V between:
i) a and b
12 
ii) b and c
iii) c and d
iv) d and a
d
6
c
b. What is the current in this circuit?
c. What power is dissipated by each resistor?
7. Consider the parallel circuit at right.
3V
a
c
a. Determine the equivalent resistance of the circuit.
b. What is the ∆V between:
i) a and b
12 
b
6
d
ii) c and d
c. What is the current in the wire leading from the battery to point a? in each of the branches?
d. How much power is dissipated by each resistor?
EM Unit 3 Worksheet 3
1. Consider the combination circuit at right.
6V
a
c
a. Determine the equivalent resistance of the circuit.
b. What is the current passing through each resistor?
12 
6
c. What is the ∆V across each resistor?
e
d. What is the power dissipated by each resistor?
8
b
d
2. Suppose the switch in the circuit at right is closed. What effect does this have on:
a. the ∆V from a to b?
6V
S
c
a
e
b. the current in the first two resistors?
6
c. the current through point g?
g
b
6
d
6
f
3. A 10 ohm and a 15 ohm resistor are connected in parallel and placed across the terminals of a
15 volt battery.
a. Sketch the circuit diagram.
b. Calculate the equivalent resistance of the circuit.
c. Calculate the current through the entire circuit.
d. Calculate the current in each branch.
4. A cabin contains only two small electrical appliances: a radio that requires 10 mA of current at
9.0 V, and a clock that requires 20 mA at 15 V. A 15 V battery with negligible internal
resistance supplies the electrical energy to operate the radio and clock.
a. Complete the diagram below to show how the
radio, clock and a single resistor R can be
connected between points A and B so that the
correct potential difference is applied across each
appliance. Use the symbols at right to indicate the
clock and radio.
radio
10mA, 9V
clock
20 mA, 15 V
A
15V
battery
B
b. Calculate the resistance of R.
c. Calculate the electrical energy that must be supplied by the battery to operate the circuit for 1
minute.
5. The electrical device whose symbol is shown at right requires a terminal
voltage of 12 V and a current of 2.0 A for proper operation.
A
24V
battery
D
Using only this device and one or more 3design a circuit so that the device will operate properly
when the circuit is connected across a 24 V battery with
negligible internal resistance.
B
6. Consider the circuit below. All the bulbs have resistance R.
a.
What is the resistance of the circuit while the switch is
open?
b.
What is the resistance of the circuit when the switch is
closed?
c. How does closing the switch affect the brightness of bulbs A and B? Explain in terms of current
and potential drop.