[ Problem View ]
Measurements in Electric Circuits
Description: Several questions related to a single-loop circuit with one resistor, an
ammeter, and a voltmeter. These devices are not necessarily considered ideal. The
students are not assumed to know the rules for series and parallel circuits; however, they
can make qualitative determinations.
Learning Goal: To understand the role of the internal resistance of various devices and
the use of the ammeter and the voltmeter.
Consider the circuit shown. All wires are considered ideal; that is, they have zero
resistance. We will assume for now that all other elements of the circuit are ideal, too:
The value of resistance
the ammeter (
is a constant, the internal resistances of the battery (
) are zero, and the internal resistance of the voltmeter (
) and
) is infinitely
large.
Part A
What is the reading
of the voltmeter?
Express your answer in terms of the EMF .
ANSWER:
= EMF
Part B
The voltmeter, as can be seen in the figure, is connected to points 1 and 3. What are the
respective voltages between points 1 and 2 and between points 2 and 3?
ANSWER:
Part C
What is the reading of the ammeter?
Express your answer in terms of and
ANSWER:
.
= EMF/R
To make things more interesting, we now assume that the battery has a nonzero internal
resistance
(the voltmeter and the ammeter remain ideal).
Part D
What is the reading of the ammeter now?
Express your answer in terms of ,
ANSWER:
, and
.
= EMF/(R+R_int)
Part E
What is the reading of the voltmeter now?
Hint E.1
Hint not displayed
Express your answer in terms of ,
ANSWER:
, and
.
= EMF*R/(R+R_int)
Now assume that the ammeter has nonzero resistance
nonzero internal resistance.
. The battery still has
Part F
Compared to their values when
voltmeter change when
, how would the readings of the ammeter and the
?
Hint F.1 How to approach this part
Hint not displayed
ANSWER:
The ammeter reading would increase; the voltmeter reading would
stay the same.
The ammeter reading would decrease; the voltmeter reading would
stay the same.
The ammeter reading would decrease; the voltmeter reading would
increase.
The ammeter reading would increase; the voltmeter reading would
increase.
Part G
What is the new reading of the ammeter?
Express your answer in terms of ,
ANSWER:
,
, and
.
= EMF/(R+R_A+R_int)
Now assume that the ammeter again has zero resistance, but the resistance of the
voltmeter is less than infinity. The battery still has nonzero internal resistance.
Part H
Compared to their values when
the voltmeter change when
, how would the readings of the ammeter and
is some large but finite value?
Hint H.1 Consider the voltmeter first
Observe that
, where is the current flowing through the battery. What
happens to the current when the resistance of the voltmeter drops?
Hint H.2 The change in the battery current
When the resistance of the voltmeter drops below infinity, it becomes possible for
current to flow both through the voltmeter and through the resistor. The overall
resistance of the circuit therefore drops, and the current through the battery increases.
How would that affect the reading of the voltmeter?
Hint H.3 The reading of the ammeter
The ammeter reading is related simply to the voltmeter reading. The current through
the ammeter is given by
, where is the voltage between points 1 and 3,
which is exactly the voltage that the voltmeter reads.
ANSWER:
The voltmeter reading would stay the same; the ammeter reading
would increase.
The voltmeter reading would stay the same; the ammeter reading
would decrease.
The voltmeter reading would decrease; the ammeter reading would
decrease.
The voltmeter reading would increase; the ammeter reading would
increase.
Suppose now that the piece of ideal wire between points 1 and 2 is removed and replaced
by a nonideal wire with a nonzero resistance.
Part I
How would this change affect the readings of the ammeter and the voltmeter?
Hint I.1
Hint not displayed
ANSWER:
The ammeter reading would stay the same; the voltmeter reading
would stay the same.
The ammeter reading would decrease; the voltmeter reading would
decrease.
The ammeter reading would increase; the voltmeter reading would
decrease.
The ammeter reading would decrease; the voltmeter reading would
increase.
The ammeter reading would increase; the voltmeter reading would
increase.
The ammeter reading would stay the same; the voltmeter reading
would increase.
[ Print ]
2:
0.1270
3: [ Problem View ]
Brightness of Light Bulbs
Description: Asks students to rank brightness of light bulbs in amixed series and parallel
circuit.
Consider a circuit containing five identical lightbulbs and an ideal battery.
Part A
Rank the brightness of the five bulbs (A through E) from brightest to dimmest. (The
more current flowing through a bulb, the brighter it will be.)
Hint A.1 Comparing bulb A to bulb B
Hint not displayed
Hint A.2 Comparing bulb D to bulb E
Hint not displayed
Hint A.3 Comparing bulb C to bulb D or E
Hint not displayed
Hint A.4 Comparing bulb C to bulb A or B
Hint not displayed
List the bulbs in order from brightest to dimmest. Between each pair of bulbs, use the
symbol > to indicate that the left-hand bulb is brighter than the right-hand bulb, or = to
indicate that the bulbs have the same brightness. For example, "B=C=E>A>D" means
that bulbs B, C, and E all have the same brightness, and that they are brighter than bulb
A, which in turn is brighter than bulb D.
ANSWER:
C>A=B>D=E
C>A=B>E=D
C>B=A>D=E
C>B=A>E=D
Now consider what happens when a switch in the circuit is opened.
Part B
What happens to bulb A?
Hint B.1 How to approach this part
How does the resistance of bulb C alone compare with the resistance of bulb C in
parallel with bulbs D and E?
How does this affect the resistance and current in the circuit as a whole (as compared
to before)?
ANSWER:
It gets dimmer.
It gets brighter.
Its brightness stays the same.
Part C
What is the current
now flowing in bulb C?
Express your answer in terms of the applied voltage and
bulb.
ANSWER:
, the resistance of a single
= (2*EMF)/(3*R)
Part D
What happens to bulb C?
Part D.1 Current in bulb C earlier
The total resistance of the earlier circuit was
bulb. What is the current
, where
is the resistance of one
flowing in bulb C?
Express your answer in terms of and
.
ANSWER: Answer not displayed
ANSWER:
It gets dimmer.
It gets brighter.
Its brightness stays the same.
This is why appliances in your home are connected only in parallel. Otherwise, turning
some on or off would cause the current in others to change, which could damage them
(typically in the case of an overload) or prevent them from functioning (if the current is
too low).
[ Print ]
4. [ Problem View ]
Batteries in Series or Parallel
Description: Computation of current through a resistor for parallel and series connected
batteries.
You are given two circuits with two batteries of emf and internal resistance
each.
Circuit A has the batteries connected in series with a resistor of resistance
B has the batteries connected in parallel to an equivalent resistor.
, and circuit
Note that the symbol should be entered in your answers as EMF.
Part A
In which direction does the current in circuit A flow?
Hint A.1 Conventions
Remember that the conventional current flows from a positive to a negative terminal.
ANSWER:
clockwise
counterclockwise
Part B
What is the current through the resistor of resistance
Hint B.1
Hint not displayed
Hint B.2
Hint not displayed
Express the current in terms of ,
, and
.
in circuit A?
ANSWER:
2*EMF/(2*R_1+R_2)
= 2*E/(2*R_1+R_2)
Part C
Calculate the current through the resistor of resistance
Hint C.1 Which rule to use
for circuit B.
Hint not displayed
Part C.2 What is the emf for loop 1?
The diagram shows the circuit divided into two loops:
branch,
is the current in the branch below it, while
is the current in the topmost
is the current in the lowest
branch, which contains . Find an expression for the emf using the voltage drops
across the two resistors in loop 1.
Express your answer in terms of
ANSWER:
,
,
, and
.
= I_3*R_2+I_1*R_1
Part C.3 What is the emf for loop 2?
Part not displayed
Part C.4 Application of Kirchhoff's junction rule (current rule)
You should now have two equations involving all the variables in the circuit diagram.
To solve for , you need a relationship between and . Choose the correct relation
by applying Kirchhoff's junction rule to one of the junctions. Recall that Kirchhoff's
junction rule states that the algebraic sum of all the currents into a junction is zero:
.
ANSWER:
Now solve the three equations you have obtained for the currents in each branch to
obtain an expression for
(
). To do this, you could either add the two equations
other than the one above, or substitute for
one.
Express your answer in terms of ,
ANSWER:
and
, and
from the other equations into this
.
2*EMF/(2*R_2+R_1)
= 2*E/(2*R_2+R_1)
Part D
What is the power dissipated by the resistor of resistance
,
, and
Hint D.1 What formula to use
for circuit A, given that
?
Hint not displayed
Calculate the power to two significant figures.
ANSWER:
= 6.40×10-2 W
Part E
For what ratio of and would power dissipated by the resistor of resistance
same for circuit A and circuit B?
Hint E.1
Hint not displayed
Hint E.2
Hint not displayed
ANSWER:
= 1.00
be the
Part F
Under which of the following conditions would power dissipated by the resistance
circuit A be bigger than that of circuit B?
Hint F.1 How to think about the problem
Hint not displayed
Some answer choices overlap; choose the most restrictive answer.
ANSWER:
[ Print ]
5.
zero
emf
clockwise
top plate
zero
=C*EMF
=EMF^2*C
=C*EMF*(1-exp(-t/(R*C)))
=EMF/R*exp(-t/(R*C))
=9.21*tau
=5.530×10-2
=q_0*exp(-t/(R*C))
=-q_0/(R*C)*exp(-t/(R*C))
6.
=(epsilon_0*r^2/d*(K-1)*V)/DeltaT
in