WileyPLUS Assignment 1
Chapters 18, 19
10 Questions, mostly “GO” with tutorial assistance
Due Thursday, January 28 at 1 am
Answers must be accurate to 2% to be “correct”.
Check the number of significant figures needed to ensure this.
Units are important when asked for. Check they’re correct.
Week of Feb 2 – 4
No labs or tests!
Wednesday, January 27, 2010
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Clicker Question
The circuit in the drawing contains three identical resistors.
Consider the equivalent resistance between the pairs of points
a and b, b and c, and a and c.
Rank the equivalent resistances in decreasing order.
A) a to b;
B) a to c;
C) a to c;
D) b to c;
E) a to b;
b to c;
b to c;
a to b;
a to c;
a to c;
Wednesday, January 27, 2010
a to c
a to b
b to c
a to b
b to c
Answer C)
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Kirchhoff’s Rules
1) Junction Rule:
! The sum of currents entering a junction is equal to the sum of
currents leaving it (conservation of charge and current).
2) Loop Rule:
! Around any closed loop, the sum of potential changes is equal
to zero (conservation of energy).
The potential decreases when you go with the flow of current
through a resistor.
– use the “conventional” flow of current
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20.-/79:
Find potential difference
between B and D
I1
I 1 – I2
I1
What is the equivalent
resistance between A and C?
I2
I2
I – I1
I 1 – I2
I
I
I – I2
I – I1
Req = V/I = 20/I
I – I2
I
What is I ?
F
E
0.94 V, A higher, Req = 42.7 !
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55
What is the equivalent resistance, Requiv ?
R
A
R
B
C
R
F
E
R
H
I
Requiv
Requiv
D
=
R
I
G
V
V
V = IRequiv
So, Requiv =
V
I
Find I by applying Kirchhoff’s rules (+ symmetry) to the original circuit
Requiv = R
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56
20.81/104: Find the current through the 2 ! resistor and the
voltage V of the battery to the left of it.
A
3A
F
B
3A
3–I
C
I
I
E
D
5 A, 46 V
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57
A galvanometer
Full scale deflection (fsd) = 0.1 mA
(for example)
Meter
Rc
Resistance of galvanometer coil
A torque is exerted on the coil when a current flows through it. The
rotation of the coil is resisted by a spring. The angle of rotation is
proportional to the current in the coil.
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58
Mode of operation of an ammeter to measure current
The ammeter is inserted into the
circuit to measure the current
flowing around the circuit.
R
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Ideally, the ammeter should have
negligible resistance so as not to
affect the current being
measured.
Rc << R
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Measurement of current –!switching scales
Ammeter – a bypass (shunt) resistor is placed
in parallel with a galvanometer to limit the
current through the galvanometer to no more
than that for full scale deflection (fsd)
To measure 60 mA when the fsd is 0.1 mA:
VAB = 0.1RC = 59.9R (mV)
galvanometer
(fsd)
So, for the shunt resistor:
R = RC
0.1
= 0.00167RC
59.9
To measure current I: R = RC
fsd
I − fsd
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60
Prob. 20.90/107: A galvanometer has a coil resistance of 12 ! and a
full scale deflection current of 0.15 mA. It is used with a shunt
resistor to make an ammeter that registers 4 mA at full scale
deflection.
Find the equivalent resistance of the ammeter.
• Work out what is the potential difference across the
galvanometer when 0.15 mA flows through it.
• Find what the shunt resistance needs to be to produce an equal
potential difference when the current flowing through the shunt
resistor is 4 – 0.15 mA.
0.45 !
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Mode of operation of a voltmeter to measure
voltage
The voltmeter is attached to two points
of a circuit between which the potential
difference is to be measured.
Ideally, the voltmeter should have very
large resistance so as to draw very little
current from the circuit being studied.
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Measurement of voltage
V = 100 V
Coil resistance
R
galvanometer
I f sd = 0.1 mA
RC = 50 ΩΩ
I = 0.1 mA
A resistor is put in series with the
galvanometer to limit the current to
that giving full scale deflection (fsd)
at the desired voltage.
To measure 100 V when fsd is at 0.1 mA and the coil resistance RC = 50 !:
V = I f sd (R + RC )
That is, R =
(R = resistance put in series with the galvanometer
to convert it to a voltmeter)
V
100 V
− RC =
− (50 !) = 999, 950 !
I f sd
0.1 × 10−3 A
R � 1 M!
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Prob. 20.89/82: Voltmeter A has an equivalent resistance of
2.4 " 105 ! and a full scale voltage of 50 V.
Voltmeter B uses the same galvanometer. It has an equivalent
resistance of 1.44 " 105 !. What is its full scale voltage?
30 V
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Ammeters and Voltmeters
Ammeter: put a resistance in
parallel with the galvanometer
to divert current from the
meter
Rc
Voltmeter: put a resistance in
series with the galvanometer
to limit the current through
the meter
Ifsd
R
R
I
I - Ifsd
Ifsd Rc = (I - Ifsd) R
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I
Ifsd
RC
V
V = Ifsd (R + Rc)
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