Transcript Chapter 19 Notes

Chapter 19
DC Circuits
© 2002, B.J. Lieb
Giancoli, PHYSICS,5/E © 1998. Electronically
reproduced by permission of Pearson Education,
Inc., Upper Saddle River, New Jersey.
Ch 19
1
Resistors in Series
•We want to find the single resistance Req that has
the same effect as the three resistors R1, R2, and
R3.
•Note that the current I is the same throughout the
circuit since charge can’t accumulate anywhere.
•V is the voltage across the battery and also
V = V1 + V 2 + V 3
•Since V1 = I R1 etc., we can say
V  V1  V2  V3  IR1  IR2  IR3
V  I ( R1  R2  R3 )
The equivalent equation is V=IReq and thus
Req  R1  R2  R3
Ch 19
2
Resistors in Parallel
This is called a parallel circuit
•Notice V1 = V2 = V3
•Since charge can’t disappear, we can say
I = I1 + I2 + I 3
•We can combine these equations with
V = IR eq to give
1
1
1
1
 

Req R1 R2 R3
Ch 19
3
Example 1
Ch 19
4
Example 2
Ch 19
5
EMF
• Devices that supply energy to an electric
circuit are referred to as a source of
electromotive force. Since this name
meaningless, we just refer to them as
source of emf (symbolized by  and a
slightly different symbol in the book.)
• Sources of emf such as batteries often have
resistance which is referred to as internal
resistance.
Ch 19
6
Terminal Voltage
a
r

b
Terminal Voltage
Vab
•We can treat a battery as a source of  in series
with an internal resistor r.
•When there is no current then the terminal
voltage is Vab= 
•But with current I we have:
V   r
•The internal resistance is small but increases with age.
Ch 19
7
Kirchhoff’s Junction Rule
•Kirchhoff’s Rules are necessary for
complicated circuits.
•Junction rule is based on conservation of
charge.
•Junction Rule: at any junction, the sum of
all currents entering the junction must equal
the sum of all currents leaving the junction.
I3
R1
R2
a
R3
2
1
Ch 19
I2
b
I1
8
Kirchhoff’s Junction Rule
•Kirchhoff’s Rules are necessary for
complicated circuits.
•Junction rule is based on conservation of
charge.
•Junction Rule: at any junction, the sum of
all currents entering the junction must equal
the sum of all currents leaving the junction.
I3
R1
R2
a
R3
2
1
Ch 19
I2
b
I1
Point a:
I1 + I2 = I 3
Point b:
I 3 = I1+ I2
9
Kirchhoff’s Loop Rule
•Loop rule is based on conservation of
energy.
•Loop Rule: the sum of the changes in
potential around any closed path of a circuit
must be zero.
I3
R1
R2
a
R3
2
1
Ch 19
I2
b
I1
10
Kirchhoff’s Loop Rule
•Loop rule is based on conservation of
energy.
•Loop Rule: the sum of the changes in
potential around any closed path of a circuit
must be zero.
I3
R1
R2
a
R3
2
1
I2
b
I1
All loops clockwise:
Upper Loop: +2 – I2 R3 – I3 R1 – I3 R2 = 0
Lower Loop: +1 + I2 R3 – 2 = 0
Large Loop: +1 – I3 R1 – I3 R2 = 0
Ch 19
11
Using Kirchhoff’s Rules
• Current:
• Current is the same in between junctions.
• Assign direction to current arbitrarily.
• If result is a negative current, it means that the
current actually flows in the opposite direction.
Don’t change direction, just give negative answer.
• Branches with a capacitor have zero current.
• Signs for Loop Rule
• Go around loop clockwise or counterclockwise.
• IR drop across resistor is negative if you are moving
in direction of the current.
• Voltage drop across battery or other emf is positive if
you move from minus to plus.
• Simultaneous Equations
• You will need one equation for each unknown.
• It pays to generate “extra” equations because they
may lead to a simpler solution.
Ch 19
12
Example 3
Ch 19
13
Capacitors in Parallel
•V is the same for each capacitor
•The total charge that leaves the battery
is
Q = Q1 + Q2 + Q3
= C1V + C2V + C3V
•Combine this with Q = Ceq V to give:
C  C1  C2  C3
Ch 19
14
Capacitors in Series
•The charge on each capacitor must be the
same.
•Thus Q = C1 V1 = C2 V2 = C3 V3
•Combine this with V = V1 + V2 + V3 to
give:
1
1
1
1
 

C C1 C2 C3
Ch 19
15
Charging a Capacitor
•When switch is closed, current flows
because capacitor is charging
•As capacitor becomes charged, the
current slows because the voltage across
the resistor is  - Vc and Vc gradually
approaches .
•Once capacitor is charged the current is
zero.
Ch 19
16
RC Decay
•If a capacitor is charged and the switch is
closed, then current flows and the voltage
on the capacitor gradually decreases.
• Since I  VC we can say that:
Q
 Q  VC
t
•It is necessary to use calculus to find:
V  V0 e
Ch 19
 t / RC
17
Exponential Decay
V  V0 e
 t / RC
•The value  = RC is called the time
constant of the decay. If R is in  and C is
in F, then  has units of seconds.
•During each time constant, the voltage
falls to 0.37 of its original value.
•We can also define the half-life (1/2) by
1/2= 0.693 RC.
•During each half-life, the voltage falls to
½ of its original value.
Ch 19
18
Example 4
Ch 19
19
Electric Hazards
•A current greater than  70 mA through the
upper torso can be lethal.
•Wet skin: I = 120 V / 1000  = 120 mA
•Dry skin: I = 120 V / 10000 = 12 mA
•Your body can act as capacitor in parallel
with resistor and this gives greater current
for ac.
•The key to safety is don’t let your body
become part of the circuit.
•Standing in water can give path to ground
which will complete circuit.
•Metal cabinet grounded by 3-prong plug
protects if there is loose wire inside because
it causes short that trips circuit breaker.
•“Ground fault detector” should turn off
current in time to protect you
Ch 19
20
Ammeters and Voltmeters
Ammeter
•To measure current it must be in circuit.
•Must have small internal resistance or it will
reduce current and confuses measurement.
Voltmeter
•To measure voltage difference, it must be
connected to two different parts of circuit.
• Must have high internal resistance or it will
draw too much current which reduces
voltage difference and confuses
measurement.
Ch 19
21