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
Series Circuit
ÎSimple
series situation
‹1
battery and two resistors R1 and R2
‹ Common current I
ÎTotal
voltage E = V1 + V2
= IR1 + IR2 ≡ IRs
‹ Rs = R1 + R2
‹E
ÎSo
equivalent resistance is the sum
‹ Works
for any number of resistors
‹ Rs = R1 + R2 + R3 + R4 + …
PHY2054: Chapter 18
5
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
6
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
7
Real EMF Sources: Internal Resistance
batteries have small internal resistance
‹ Lowers
effective potential delivered to circuit
V0
i=
r+R
Vb
r
V0
Veff = Vb − Va = V0 − ir
R
C
V0
r
= V0 −
r+R
R
= V0
r+R
Va
Veff
C
ÎReal
V0
=
1+ r / R
This is the voltage measured across the terminals!
PHY2054: Chapter 18
8
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
Lose 0.01 V
ÎV0 =
ÎV0
V0
=
1+ r / R
12V, r = 0.1Ω, R = 10Ω
Lose 0.1 V
= 12V, r = 0.1Ω, R = 1Ω
ÎV0 =
Veff = 12 /1.01 = 11.9 V
12V, r = 0.1Ω, R = 0.5Ω
Veff = 12 /1.1 = 10.9 V
Lose 1.1 V
Veff = 12 /1.2 = 10.0 V
Lose 2.0 V
PHY2054: Chapter 18
9
Heating From Internal Resistance
ÎHeating
of EMF source: P = i2r
is extremely dependent on load
‹ You can feel battery getting warm when 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
10
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
11
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
12
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
13
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
14
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
15
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.
16
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
17