section 15.4 series and parallel circuits
TRANSCRIPT
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Section 15.4Section 15.4
Series and parallel circuitsSeries and parallel circuits
Section 15.4Section 15.4
Series and parallel circuitsSeries and parallel circuits
Parallel circuitParallel circuit
Series circuitSeries circuit
Effects of resistance ofEffects of resistance of
ammeter, voltmeter and cellammeter, voltmeter and cell
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Series and parallel circuits
Bulbs are connected in two ways:
15.4 Series and parallel circuits (SB p. 55)
Go to
Discussion 2Discussion 2
Go to
Discussion 3Discussion 3
in series
in parallel
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Series circuit
Series circuit connects electricalcomponents one by one, forming single loop
15.4 Series and parallel circuits (SB p. 56)
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total electrical energysupplied by the cell (E)
Series circuit
15.4 Series and parallel circuits (SB p. 57)
electrical energy
dissipated inX(E1)
electrical energy
dissipated in Y(E2)
By ,
V= V1 + V2
Q
EV =
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Resistance in series circuit
15.4 Series and parallel circuits (SB p. 57)
VVV
III
=+
==
21
21
( )IIIRRR
RIRIIR
VVV
==+=
+=
+=
2121
2211
21
As
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Resistance in series circuit
15.4 Series and parallel circuits (SB p. 57)
equivalent resistance
R= R1 + R2 + R3 + R4 +
CALWorkshop 5
Simple circuits
(A) Series
circuit
http://cal/E-SimPhy_405.exe -
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Resistance in series circuit
15.4 Series and parallel circuits (SB p. 58)
Drawback of
series circuit
one bulb burns out
whole circuit breakdown
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Resistance in series circuit
15.4 Series and parallel circuits (SB p. 58)
Drawback of
series circuit
undesirable for domestic wiring
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Parallel circuit
Parallel circuit splits into branches withconnected electrical components
15.4 Series and parallel circuits (SB p. 58)
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Resistance in parallel circuit
15.4 Series and parallel circuits (SB p. 59)
21 VVV ==
21
21
21
21
21
or
111
As
RR
RRR
RRR
R
V
R
V
R
V
III
+
=
+=
+=
+=
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Resistance in parallel circuit
15.4 Series and parallel circuits (SB p. 59)
equivalent resistance
...++++=
4321
11111
RRRRR
CALWorkshop 6
Simple circuits
(B) Parallel
circuit
http://cal/E-SimPhy_405.exe -
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Resistance in parallel circuit
15.4 Series and parallel circuits (SB p. 60)
Use for domestic wiring
Thinking 2Thinking 2
failure of one bulb
not affect others
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Example 2:Example 2:In the circuit, a battery of voltage of 9 V is connected to a
rheostat. The resistance ofACis 10 and that ofAB is4 .
15.4 Series and parallel circuits (SB p. 60)
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Example 2: (Cont)Example 2: (Cont)(a) What is the current in the circuit? Solut
ionLet the current in the circuit beI. The voltage acrossAC
is 9 V. The resistance of the circuit is 10 .
By
I= 0.9 A
I
I
VR
910 =
=
15.4 Series and parallel circuits (SB p. 60)
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Example 2: (Cont)Example 2: (Cont)(b) What is the voltage acrossAB?
(c) What is the voltage across BC?
Solut
ionThe current flowing throughAB is 0.9 A. The resistance
is 4 .
By V =IR
V = 0.9 4 = 3.6 V
15.4 Series and parallel circuits (SB p. 60)
Solut
ionVoltage acrossBC= 9 3.6 = 5.4 V
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Example 3:Example 3:In the circuit as shown, find
(a) the total resistance of the resistors
Solution
15.4 Series and parallel circuits (SB p. 61)
Thinking 3Thinking 3
Resistance of the 3- and 6- resistors = = 2
Total resistance = 2 + 4 = 6 63
63
+
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Example 3: (Cont)Example 3: (Cont)(b) find the current flowing through the 4- resistor,
(c) find the currents flowing through the 3- and 6- resistors,
Solut
ionCurrent through the 4- resistor = = 0.5 A6
3=
R
V
15.4 Series and parallel circuits (SB p. 61)
Solut
ion
Voltage across the 3- and 6- resistors =IR = 0.5 2 = 1
V
Current flowing through the 3- resistor
Current flowing through the 6- resistor
A3
1==
R
V
A6
1==
R
V
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Example 3: (Cont)Example 3: (Cont)(d) find the voltage across the 4- resistor.
SolutionVoltage across the 4- resistor = IR = 0.5 4 = 2 V
15.4 Series and parallel circuits (SB p. 61)
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Class Practice 3:Class Practice 3:In the circuit, a 100- and a 300- resistors are
connected in parallel with a cell of 20 V.
(a) Find the total resistance of the resistors.
________________
Total resistance = _________________
Ans
wer
75
15.4 Series and parallel circuits (SB p. 61)
=+=
21
111
RRR 300
1
100
1+
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Class Practice 3: (Cont)Class Practice 3: (Cont)(b) Find the current drawn from the cell.
Current drawn from the cell (I) =
______________
(c) Find the current passing through each resistor.
Current passing through 100- resistor
_________________
Current passing through 300- resistor
_________________
Ans
wer
15.4 Series and parallel circuits (SB p. 62)
=
R
VA27.0
75
20=
A2.0100
20==
R
V
A07.0300
20==
R
VAns
wer
Ans
wer
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Class Practice 4:Class Practice 4:(a) In the circuit, find the total resistance.
Ans
wer
15.4 Series and parallel circuits (SB p. 62)
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Class Practice 4: (Cont)Class Practice 4: (Cont)
15.4 Series and parallel circuits (SB p. 62)
Since the 100- and 200- resistors
are connected in series.
Total resistance of the 100- and 200- resistors
= 100 + 200 = 300 The 300- resistor connected with them in parallel, by
Total resistance of the 100- , 200- and 300- resistors = 150
300
1
300
11+=
R
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Class Practice 4: (Cont)Class Practice 4: (Cont)(b) Find the total current drawn from the cell.
The current drawn from the cell
________________
(c) Find the currents flowing through each of the resistors.
Ans
wer
15.4 Series and parallel circuits (SB p. 62)
A2.0150
30==
R
V
Ans
werThe current flowing through the 100- and 200- resistors
The current flowing through the 300- resistor
A1.0
300
30===
R
V
A1.0300
30===
R
V
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Class Practice 4: (Cont)Class Practice 4: (Cont)(d) Find the voltage across each of the resistors.
Ans
wer
Voltage across the 100- resistor
=IR = 0.1 100 = 10 V
Voltage across the 200- resistor
=IR = 0.1 200 = 20 V
Voltage across the 300- resistor= 30 V
15.4 Series and parallel circuits (SB p. 63)
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Effects of resistance of ammeter,
voltmeter and cell
15.4 Series and parallel circuits (SB p. 63)
They have resistance too
effect on current / voltage
Go to
Discussion 4Discussion 4
battery
ammeter
voltmeter
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Effects of resistance of ammeter
15.4 Series and parallel circuits (SB p. 64)
( few ohms )
Small resistance circuit
Total resistance= Resistance ofR1+ Resistance of ammeter (RA)
comparable total resistance
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Effects of resistance of ammeter
15.4 Series and parallel circuits (SB p. 64)
resistance
Small resistance circuit
I & V of R1
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Effects of resistance of ammeter
15.4 Series and parallel circuits (SB p. 64)
Total resistance= Resistance ofR2+ Resistance of ammeter (RA)
Large resistance circuit
R2 >>RAtotal resistanceremain unchanged
I & V of R2
remain
unchanged
( few ohms )
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Effects of resistance of voltmeter
15.4 Series and parallel circuits (SB p. 65)
Total current= Current through R1+ Current through voltmeter
Small resistance circuit
RV >>R1total currentremain unchanged
( few hundred ohms )
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15.4 Series and parallel circuits (SB p. 65)
Large resistance circuit
Total current= Current through R1+ Current through voltmeter
RV &R1 comparable total current
Effects of resistance of voltmeter
( few hundred ohms )
i d ll l i i ( )
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15.4 Series and parallel circuits (SB p. 66)
internal resistance (r) (few ohms)
Voltage of the cell =I
(R
+r
)
affects V&Iofsmall resistance circuit only
Effect of resistance of cell
Thinking 4Thinking 4
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To section 15.5
15 4 S i d ll l i it (SB 55)
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Discussion 2:Discussion 2:
When one of the light bulbs on a Christmas tree isremoved, what happen to the other light bulbs? Why?
The light bulbs in the affected string
do not light up but the light bulbs in
other strings do. This is because the
unlit bulbs are connected in series. If
one light bulb is failed, the other
bulbs do not light up. However, theother light bulbs in different strings
are connected in parallel. Therefore,
they still light up.
Ans
wer
15.4 Series and parallel circuits (SB p. 55)
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TextText
15 4 S i d ll l i it (SB 56)
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Discussion 3:Discussion 3:
You are given two resistors, a dry cell and someconnecting wires.
Connect the resistors (a) in series and (b) in parallel
with the dry cell to form a closed circuit. In each case,
(i) draw the circuit diagram,
(ii) find the relation between the currents passing
through the dry cell and the two resistors, and
(iii) find the relation between the voltages across the
dry cell and the two resistors.
15.4 Series and parallel circuits (SB p. 56)
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Discussion 3:Discussion 3:(Cont)(Cont)
(Hint: Imagine the electric circuit as a water pipesystem with the dry cell acting as a pump, the
connecting wires as pipes, the current as a flow of
water and resistors as water turbines.)
(a) In series
Ans
wer
15.4 Series and parallel circuits (SB p. 56)
(ii)I1 =I2 =I3(iii) V1 = V2 + V3
(a)(i)
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Discussion 3:Discussion 3:(Cont)(Cont)
(b) In parallel
Ans
wer
15.4 Series and parallel circuits (SB p. 56)
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TextText
(ii)I1 =I2 +I3
(iii) V1 = V2 = V3
(b)(i)
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Thinking 2Thinking 2
Injury caused by an electric shock depends onthe amount of the current that flows in the
body. Why do we see signs that read
"Danger - High Voltage" rather than
"Danger - High Current"? Answer
This is because the current depends on
the resistance of the body. The voltage
is fixed by the power source. Therefore awarning of high voltage is more relevant
than that of high current.Return to
TextText
15.4 Series and parallel circuits (SB p. 60)
15 4 Series and parallel circuits (SB p 61)
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Thinking 3Thinking 3
In the circuit, when the switch is closed, whathappen to the readings of ammetersA1,A2
and voltmeterV1?
15.4 Series and parallel circuits (SB p. 61)
Ans
wer
15 4 Series and parallel circuits (SB p 61)
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Thinking 3 (Cont)Thinking 3 (Cont)
The reading ofV1 remains unchanged because it is
equal to the voltage of the cell. The voltage acrossR1 is
equal to the voltage of the cell. ByI
= , the reading ofA1 remains unchanged.
The reading ofA2 is equal to the sum of the current
passing throughR1 andR2. If the switch is closed, there
is a current passing throughR2. Therefore, the reading
ofA2 increases.
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TextText
15.4 Series and parallel circuits (SB p. 61)
R
V
15 4 Series and parallel circuits (SB p 63)
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Discussion 4:Discussion 4:
1. In CircuitA, find the voltages across theresistor (R) and currents passing through it if the
resistance ofRis
(a) 0.1 , and
(b) 1 k .
15.4 Series and parallel circuits (SB p. 63)
Ans
wer
(a) VA1 = 3 V
IA1 = = 30 A1.0
3
(b) VA2 = 3 V
IA2 = = 3 103 A
k1
3
CircuitA
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Discussion 4: (Cont)Discussion 4: (Cont)2. In Circuit B, find the voltages across the resistor
(R) if the resistance ofRis
(a) 0.1 , and
(b) 1 k .
15.4 Series and parallel circuits (SB p. 63)
Ans
wer
IB1 = = 0.588 A
VB1
= 0.588 0.1
= 0.0588 V
51.0
3
+
(a)IB2 = = 2.985 10
3A
VB2
= 2.985 103 1 k
= 2.985 V
5k1
3
+
(b)
CircuitB
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Discussion 4: (Cont)Discussion 4: (Cont)3. In Circuit B, if we take the 5- resistor away,
what happen to the voltage and the current in resistor
R?
15.4 Series and parallel circuits (SB p. 63)
Ans
wer
CircuitB becomesCircuitA.
(i) If the resistor ofR is
small (e.g., 0.1 ),
IA1 >>IB1VA1 >>VB1
(ii) If the resistance ofR is
large (e.g., 1 k ),
IA2 IB2VA2 VB2
CircuitB
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Discussion 4: (Cont)Discussion 4: (Cont)
44. In Circuit C, find the total currents flowing out ofthe battery if the resistance ofRis(a) 0.1 , and
(b) 1 k .
15.4 Series and parallel circuits (SB p. 64)
Ans
wer
(a) IC1 =
= 30.000 A
k103
1.03 + (b) IC2 =
= 3.3 103 A
k103
k13 +
Circuit C
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Discussion 4: (Cont)Discussion 4: (Cont)5. In Circuit C, if we take the 10- k resistor away,
what happens to the current flowing through resistor
R?
p ( p )
Circuit Calso becomes
CircuitA.
(i) If the resistor ofR is
small (e.g., 0.1
),IA1 IC1
(ii) If the resistance ofR is
large (e.g., 1 k
),IA2
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Thinking 4Thinking 4
The resistance of a resistor can be found byusing either circuitA or circuit B shown below.
Explain which circuit is suitable for finding
1. high resistance and
2. low resistance.Ans
wer
p ( p )
R R
Circuit BCircuitA
15.4 Series and parallel circuits (SB p. 66)
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Thinking 4 (Cont)Thinking 4 (Cont)
1. CircuitAVoltmeter reading = VacrossR + Vacross ammeter
SinceRresistor >>Rammeter and VR,
VacrossR >> Vacross ammeter.So VacrossR ~ voltmeter reading.
Ammeter reading =IthroughR
Therefore, the resistance calculatedfromR = V/Iis close to the actual value.
p ( p )
R
R15.4 Series and parallel circuits (SB p. 66)
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Thinking 4 (Cont)Thinking 4 (Cont)
2. CircuitB
Ammeter reading =IthroughR +Ithrough voltmeter
SinceRresistor Ithrough voltmeter.
ThereforeIthroughR ~ ammeter reading.
Voltmeter reading = VacrossR
Therefore, the resistance calculated
fromR = V/Iis close to the actual value.
In an ideal case, we should always use an ammeter with a very low
resistance and a voltmeter with an extremely high resistance. Then,
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R