Circuits
PHY2054: Chapter 18
1
What You Already Know
ÎMicroscopic
ÎDrift
nature of current
speed and current
ÎOhm’s
law
ÎResistivity
ÎCalculating
ÎPower
resistance from resistivity
in electric circuits
PHY2054: Chapter 18
2
Chapter 18: Electric Circuits
ÎWork,
energy and EMF
ÎSingle
loop circuits
ÎMultiloop
circuits
ÎAmmeters
ÎRC
and voltmeters
circuits and time constant
PHY2054: Chapter 18
3
Reading Quiz for Chapter 18
ÎWhen
resistors are connected in series
‹ (1)
the current in each resistor is different
‹ (2) the current in each resistor is the same
‹ (3) the voltage in each resistor is the same
ÎWhich
of the following is not related to Kirchhoff’s Rules?
‹ (1)
conservation of charge
‹ (2) conservation of energy
‹ (3) conservation of momentum
PHY2054: Chapter 18
4
Resistors in series
ÎEMF
of battery is 12 V, 3 identical resistors. What is the
potential difference across each resistor?
‹ 12
V
‹0 V
‹3 V
‹4 V
Equal resistances, 4V across each one
PHY2054: Chapter 18
5
Resistors in series
ÎAll
light bulbs are identical in these two circuits. Which
circuit has the higher current?
‹ circuit
A
‹ circuit B
‹ both the same
ÎWhich
circuit has larger total brightness?
‹ circuit
A
‹ circuit B
‹ both the same
A
Current in A is twice that of B
Brightness in each bulb in B is ¼ A
so total brightness of B is ½ A
B
PHY2054: Chapter 18
6
Real EMF Sources: Internal Resistance
batteries have small internal resistance
‹ Lowers
effective potential delivered to circuit
V0
i=
r+R
Vb
r
Va
V0
Veff = Vb − Va = V0 − ir
R
V0
= V0 −
r
r+R
C
Veff
C
ÎReal
V0
=
1+ r / R
This is the voltage measured across the terminals!
PHY2054: Chapter 18
7
Internal Resistance Example
ÎLoss
of voltage is highly dependent on load
Veff
ÎV0
= 12V, r = 0.1Ω, R = 100Ω Veff = 12 /1.001 = 11.99 V
‹ Loss
ÎV0 =
of 0.01V
12V, r = 0.1Ω, R = 10Ω
‹ Loss
ÎV0
V0
=
1+ r / R
of 0.1V
= 12V, r = 0.1Ω, R = 1Ω
‹ Loss
ÎV0 =
Veff = 12 /1.1 = 10.9 V
of 1.1V
12V, r = 0.1Ω, R = 0.5Ω
‹ Loss
Veff = 12 /1.01 = 11.9 V
of 2.0V
Veff = 12 /1.2 = 10.0 V
PHY2054: Chapter 18
8
Heating From Internal Resistance
ÎHeating
of EMF source: P = i2r
is extremely dependent on load
‹ You can feel battery warm when it is used at high current
‹ Heating
Vba
ÎV0
V0
=
1+ r / R
V0
i=
r+R
P = i 2r
= 12V, r = 0.1Ω
‹R
=
‹R =
‹R =
‹R =
100Ω
10Ω
1.0Ω
0.5Ω
Vba
Vba
Vba
Vba
=
=
=
=
11.99V
11.9V
10.9V
10.0V
i
i
i
i
=
=
=
=
0.12 A
1.19 A
10.9 A
20 A
PHY2054: Chapter 18
P
P
P
P
=
=
=
=
0.0014 W
0.14 W
11.9 W
40 W
9
Resistors in Parallel
Î Current
splits into several branches.
Total current is conserved
‹
i = i1 + i2
Î Potential
resistor
‹
difference is same across each
V = V1 = V2
a
I
V
d
V
V V
=
+
R p R1 R2
a
I2
R1
R2
I
I
I
V
1
1
1
=
+
R p R1 R2
I1
Rp
d
I
Rp = equivalent resistance
PHY2054: Chapter 18
10
Resistors in Parallel
ÎAs
more resistors R are added in parallel to the circuit, how
does total resistance between points P and Q change?
‹ (a)
increases
‹ (b) remains the same
‹ (c) decreases
ÎIf
the voltage between P & Q is
held constant, and more resistors
are added, what happens to
the current through each resistor?
‹ (a)
increases
‹ (b) remains the same
‹ (c) decreases
Overall current increases,
but current through each
branch is still V/R.
PHY2054: Chapter 18
11
Household Circuits
ÎDevices
added in parallel
‹ Each
device sees full 120 V
‹ Each current is i = 120/Ri
ÎOverload:
too many devices
can draw more current than
house wires can handle.
‹ Overheating
of wires
‹ Fire
hazard!
‹ Circuit breaker protects against
this happening
PHY2054: Chapter 18
12
Example: Equivalent Resistance
ÎWhat
is the net resistance of the circuit connected to the
battery? Each resistance has R = 3Ω
‹ R1,
‹ R3
‹ R4
‹ R5
‹ R6
R2 in series ⇒ R12 = 6Ω
in parallel with R12 ⇒ R123 = 2Ω
in series with R123 ⇒ R1234 = 5Ω
in parallel with R1234⇒ R12345 = 1.875Ω
in series with R12345 ⇒ R123456 = 4.875Ω
2
1
4
3
5
6
PHY2054: Chapter 18
13
Circuits
ÎIf
the light bulbs are all the same in each of these two
circuits, which circuit has the higher current?
‹ (a)
circuit A
B draws twice the
‹ (b) circuit B
current as A
‹ (c) both the same
ÎIn
which case is each light bulb
brighter?
A
Current through each
circuit A
branch is unchanged (V/R)
‹ (b) circuit B
‹ (c) both the same
‹ (a)
B
PHY2054: Chapter 18
14
Light Bulb Problem
ÎTwo
light bulbs operate at 120 V, one with a power rating
of 25W and the other with a power rating of 100W.
Which one has the greater resistance?
‹ (a)
the one with 25 W
‹ (b) the one with 100 W
‹ (c) both have the same resistance
ÎWhich
carries the greater current?
‹ (a)
the one with 25 W
‹ (b) the one with 100 W
‹ (c) both have the same current
P = I2R = V2/R, where V is the
same for both. 100W bulb has
¼ the resistance of the 25W bulb
and carries 4x the current.
15
PHY2054: Chapter 18
Dimmer
ÎAssume
a dimmer consisting of a variable resistor is put in
series with a bulb. When you rotate the knob of a light
dimmer, what is being changed in the electric circuit?
‹ (a)
‹ (b)
‹ (c)
‹ (d)
‹ (e)
the voltage in the circuit
the resistance
the current
House voltage is always ~120 V.
both (a) and (b)
Turning the knob increases the circuit
both (b) and (c)
resistance and thus lowers the current.
Note that this is a bad design for a
Dimmer. Why?
PHY2054: Chapter 18
16
Power lines
ÎAt
large distances, the resistance of power lines becomes
significant. To transmit maximum power, is it better to
transmit high V, low I or high I, low V?
‹ (a)
high V, low I
‹ (b) low V, high I
‹ (c) makes no difference
ÎWhy
Power loss is I2R, so want
to minimize current.
do birds sitting on a high-voltage power line survive?
‹ They
are not touching high and low potential simultaneously to
form a circuit that can conduct current
PHY2054: Chapter 18
17
Resistors
ÎCurrent
flows through a light bulb. If a wire is now
connected across the bulb as shown, what happens?
‹ (a)
Bulb remains at same brightness
‹ (b) Bulb dims to 1/4 its former brightness (1/2 current)
‹ (c) Bulb goes out
‹ (d) None of the above
The wire “shunt” has almost no resistance and
it is in parallel with a bulb having resistance.
Therefore voltage across shunt (and bulb ) is ~ 0.
Thus almost all the current follows the zero
(or extremely low) resistance path.
PHY2054: Chapter 18
18
Circuits
ÎTwo
light bulbs A and B are connected in series to a
constant voltage source. When a wire is connected across
B, what will happen to bulb A?
‹ (a)
burns more brightly than before
‹ (b) burns as brightly as before
‹ (c) burns more dimly than before
‹ (d) goes out
The wire shunt effectively eliminates the
second resistance, hence increasing the
current in the circuit by 2x. The first
bulb burns 4x brighter (I2 R).
PHY2054: Chapter 18
19
Circuits
ÎConsider
the network of resistors shown below. When the
switch S is closed, then:
‹ What
happens to the voltage across R1, R2, R3, R4?
‹ What happens to the current through R1, R2, R3, R4?
‹ What happens to the total power output of the battery?
‹ Let R1 = R2 = R3 = R4 = 90 Ω and V = 45 V. Find the current
through each resistor before and after closing the switch.
Before
¾I1 = 45/135 = 1/3
¾I2 = 0
¾I3 = I4 = 15/90=1/6
After
¾I1 = 45/120 = 3/8
¾I2 = I3 = I4 = 1/8
PHY2054: Chapter 18
20