Electricity and Magnetism
DC Circuits
Using with Kirchhoff’s Laws
Lana Sheridan
De Anza College
Oct 23, 2015
Last time
• grounding a circuit
• household wiring
Overview
• Kirchhoff’s laws practice
• meters
Potential
an ideal, resistance-free em
resistance
R is connected a
difference between two points
through the battery from
V e
locations. Passing from the
r
R
a b c
d
e
f
increases by an amount .
tial decreases by an amount
e
terminal voltage of the bat
Ir
a
e
IR
From this expression, noti
is, the terminal voltage wh
a battery; for example, the
“Voltage Drops”:
b
between a battery’s termin
resistance rule
Equation 28.1. Figure 28.1
Figure 28.1 (a) Circuit diagram
of a source of emf e (in this case,
potential
as the
Going through a resistance
R in the direction of the
current,
thecircuit is tr
a battery), of internal resistance
Figure 28.1a shows that
change in potential isr, connected
−IR; intothe
opposite
an external
resis-direction it is +IR.
ence across the external res
tor of resistance R. (b) Graphical
tor might be a simple resis
“Voltage jumps”: representation showing how the
resistance of some electric
electric potential changes as the
circuit in (a) is traversed clockwise.
emf rule
connected to the battery (
resistor represents a lo
Going through an ideal emf device in the directionThe
of the
emf
to operate the device conta
arrow, the change in potential is +E; in the opposite
direction
is 5 IR. C
load resistance it
is DV
0
−E.
Kirchhoff’s Laws
Loop Rule
The sum of the changes in potential encountered in a complete
traversal of any loop of a circuit must be zero.
Junction Rule
The sum of the currents entering any junction must be equal to
the sum of the currents leaving that junction.
Example with Two Batteries
Find the current in the circuit.
gure 28.14.
circuit.
e1 # 6.0 V
a
! "
R 2 # 10 $
uess at the
he current
tion of the
ss is repre-
d
I
b
R 1 # 8.0 $
! "
e2 # 12 V
c
Figure
28.14
28.6)
Suppose the current
flows
in the (Example
direction shown.
it, but let’s
A series circuit containing two
Example with Two Batteries
own in Figure 28.14.
nt in the circuit.
and a guess at the
two, so the current
the direction of the
rrect guess is repre-
e1 # 6.0 V
a
! "
R 2 # 10 $
d
I
b
R 1 # 8.0 $
! "
e2 # 12 V
c
Figure 28.14 (Example 28.6)
XA series circuit containing two
ple circuit, but let’s
∆V = Eand
IR1resistors,
− E2 − IR2 = 0
1 −two
batteries
no junctions in this
where the polarities of the batnts.
teries are in opposition.
e 28.14. Traversing the circuit in the clockwise direcnce of 1e 1 , b S c represents a potential difference of
Example with Two Batteries
own in Figure 28.14.
nt in the circuit.
and a guess at the
two, so the current
the direction of the
rrect guess is repre-
e1 # 6.0 V
a
! "
R 2 # 10 $
d
I
b
R 1 # 8.0 $
! "
e2 # 12 V
c
Figure 28.14 (Example 28.6)
XA series circuit containing two
ple circuit, but let’s
∆V = Eand
IR1resistors,
− E2 − IR2 = 0
1 −two
batteries
no junctions in this
where the polarities of the batnts.
teries are inEopposition.
1 − E2
⇒ I=
= −0.33 A
R1 + R2
e 28.14. Traversing the circuit in the clockwise direcMinus sign means that the current flows opposite to the direction
nce of 1e 1 , b S c represents a potential difference of
shown in the diagram.
R2
2
pation rate
(b) resistor
(4.0and
") and
batteries
haveinemfs
!1 ! 121 V
!2 !(c) –
R1
2 (8.0
"), the
and
the energy
Using
Laws
examples
1
6.0resistor
V. Kirchhoff’s
What
are (a)
current,
the transfer
dissi- +
rate
in
(d)
battery
1
and
(e)
battery
2?
Is
R2
2
pation rate in (b) resistor 1 (4.0 ") and (c) –
– +
energy
being
supplied
or
absorbed
by
(f)
resistor 2 (8.0 "), and the energy transfer
1
battery
1battery
and#2
(g) 1battery
2? battery 2? Is
Fig. 27-25
rate
in (d)
and (e)
Page
726,
Problem
1.
– +
•2 In
Fig. supplied
27-26, the
batteries
energy
being
orideal
absorbed
by (f)
have 1emfs
!1 !
150 V2?
and !2 ! 50 V Q
battery
and (g)
battery
Fig. 27-25
and the resistances are R1 ! 3.0 "
R1
Problem
1.
•2 In Fig. 27-26, the ideal batteries
and R2 ! 2.0 ". If the potential at P is –
–
have emfs !1 ! 150 V and !2 ! 50 V Q
100 V, what is it at Q?
1
2
+
+
and the resistances are R1 ! 3.0 "
R1
battery
withataP12
and•3R2ILW
! 2.0A".car
If the
potential
is V –
R2
–
and an
internal
100emf
V, what
is it
at Q? resistance of 0.040 +
1
2
+ P
" is being charged with a current of 50
•3 ILW A car battery with a 12 V
R 2 Problem 2.
A. What are (a) the potential differ- Fig. 27-26
emf and an internal resistance of 0.040
P
ence V across the terminals, (b) the
" is being charged with a current of 50
rate P of energy dissipation inside the battery, and (c) the rate P
A. Whatr are (a) the potential differ- Fig. 27-26 Problem 2. emf
of energy conversion to chemical form? When the battery is used to
ence
V across the terminals, (b) the
supply 50 A to the starter motor, what are (d) V and (e) Pr?
rate Pr of energy dissipation inside the battery, and (c) the rate Pemf
of energy conversion to chemical form? When the battery is used to
supply 50 A to the starter motor, what are (d) V and (e) Pr?
tric
of t
R2
2
pation rate
(b) resistor
(4.0and
") and
batteries
haveinemfs
!1 ! 121 V
!2 !(c) –
R1
2 (8.0
"), the
and
the energy
Using
Laws
examples
1
6.0resistor
V. Kirchhoff’s
What
are (a)
current,
the transfer
dissi- +
rate
in
(d)
battery
1
and
(e)
battery
2?
Is
R2
2
pation rate in (b) resistor 1 (4.0 ") and (c) –
– +
energy
being
supplied
or
absorbed
by
(f)
resistor 2 (8.0 "), and the energy transfer
1
battery
1battery
and#2
(g) 1battery
2? battery 2? Is
Fig. 27-25
rate
in (d)
and (e)
Page
726,
Problem
1.
– +
•2 In
Fig. supplied
27-26, the
batteries
energy
being
orideal
absorbed
by (f)
have 1emfs
!1 !
150 V2?
and !2 ! 50 V Q
battery
and (g)
battery
Fig. 27-25
and the resistances are R1 ! 3.0 "
R1
Problem
1.
•2 In Fig. 27-26, the ideal batteries
and R2 ! 2.0 ". If the potential at P is –
–
have emfs !1 ! 150 V and !2 ! 50 V Q
100 V, what is it at Q?
1
2
+
+
and the resistances are R1 ! 3.0 "
R1
battery
withataP12
and•3R2ILW
! 2.0A".car
If the
potential
is V –
R2
–
and an
internal
100emf
V, what
is it
at Q? resistance of 0.040 +
1
2
+ P
" is being charged with a current of 50
•3 ILW A car battery with a 12 V
R 2 Problem 2.
A. What are (a) the potential differ- Fig. 27-26
emf and an internal resistance of 0.040
P
encerule:
V across
(b) =the
−E2 −the
IR2terminals,
E1 − IR
0, I = 20 A.
"Loop
is being
charged
with
a+current
of1 50
rate P of energy dissipation inside the battery, and (c) the rate P
A. Whatr are (a) the potential differ- Fig. 27-26 Problem 2. emf
of
energyatconversion
Potential
Q = −10 to
V.chemical form? When the battery is used to
ence
V across the terminals, (b) the
supply 50 A to the starter motor, what are (d) V and (e) Pr?
rate Pr of energy dissipation inside the battery, and (c) the rate Pemf
of energy conversion to chemical form? When the battery is used to
supply 50 A to the starter motor, what are (d) V and (e) Pr?
tric
of t
Example with a Multiloop Circuit
Find the currents I1 , I2 , and I3 in the circuit.
14.0 V
e
f
" #
4.0 !
b
(Example
ircuit containing
branches.
I1
# "
10.0 V
28.15
I2
6.0 !
a
2.0 !
c
I3
d
Suppose the currents flow in the direction shown.
in Figure
28.15.
Example with a Multiloop Circuit
Junction rule:
I1 + I2 = I3
(1)
10V − (6Ω)I1 + (2Ω)I3 = 0
(2)
−14V + (6Ω)I1 − 10V − (4Ω)I2 = 0
(3)
−14V − (2Ω)I3 − (4Ω)I2 = 0
(4)
Loops:
Example with a Multiloop Circuit
14.0 V
e
f
" #
4.0 !
b
A circuit containing
rent branches.
I1
# "
10.0 V
re 28.15 (Example
I2
6.0 !
a
2.0 !
c
I3
d
led in Figure 28.15.
1 I2 2 I3 5 0
I1 = +2.0 A I2 = −3.0 A I3 = −1.0 A
(a)
(b)
Using Kirchhoff’s Laws
examples
Fig. 27-20 Question 5.
(c)
6 Res-monster maze. In Fig. 27-21, all the resistors have a
resistance of 4.0 $ and all the (ideal) batteries have an emf of 4.0
V. What is the current through resistor R? (If you can find the
proper loop through this maze, you can answer the question with a
few seconds of mental calculation.)
(b) Are
sistances
to a batel. Rank
through
R
x
e
stion 4.
Fig. 27-21
Question 6.
rent i1 through R1 now more than, less than, or the same as previ-
Using ously?
Kirchhoff’s
Laws resistance
examples
(c) Is the equivalent
R12 of R1 and R2 more than,
less than, or equal to R1?
8 Cap-monster maze. In Fig. 27-22, all the capacitors have a
capacitance of 6.0 mF, and all the batteries have an emf of 10 V.
What is the charge on capacitor C? (If you can find the proper loop
through this maze, you can answer the question with a few seconds
of mental calculation.)
C
Fig. 27-22
Question 8.
R2 more
through
current t
10 Aft
closed on
through
gives tha
values of
and C0, (
2C0, (4) 2
with whic
11 Figu
tions of
nected in
via a swi
capacito
rium) ch
capacito
Summary
• Kirchhoff’s laws practice
• loop circuits
Next Test on Oct 30.
Homework
• Collected homework 2, posted online, due on Monday, Oct 26.
Serway & Jewett:
• PREVIOUS: Ch 28, onward from page 857. Problems: 5, 9,
15, 27, 31, 47
• NEW: Ch 28. Problems: 33, 35