Capacitors in a Circuit
emf
Resistors
series
parallel
Circuit problems
Capacitors in a circuit
Reading Question
Electrical power is
1.
2.
3.
4.
5.
6.
P = IV
P = Ed
P = I2R
P = qV
None of the above.
Two or more of the above.
Reading
Question
Electrical power is
1.
2.
3.
4.
5.
6.
P = IV
P = Ed
P = I2R
P = qV
None of the above.
Two or more of the above.
Reading Question
What property of a real battery makes its potential
difference slightly different than that of an ideal battery?
1. Short circuit
2. Chemical potential
3. Internal resistance
4. Effective capacitance
5. Inductive constant
Reading Question
What property of a real battery makes its potential
difference slightly different than that of an ideal battery?
1. Short circuit
2. Chemical potential
3. Internal resistance
4. Effective capacitance
5. Inductive constant
Reading Question
In an RC circuit, what quantity is
represented by the symbol
1. Period
2. Torque
3. Terminal voltage
4. Time constant
5. Coefficient of thermal expansion
Reading Question
In an RC circuit, what quantity is
represented by the symbol
1. Period
2. Torque
3. Terminal voltage
4. Time constant
5. Coefficient of thermal expansion
Reading Question
The equivalent resistance for a group of series resistors is
1. less than any resistor in the group.
2. equal to the smallest resistance in the group.
3. equal to the average resistance of the group.
4. larger than any resistance in the group.
5. larger than any resistor in the group.
Reading Question
The equivalent resistance for a group of series resistors is
1. less than any resistor in the group.
2. equal to the smallest resistance in the group.
3. equal to the average resistance of the group.
4. larger than any resistance in the group.
5. larger than any resistor in the group.
Student Workbook
emf
emf
Student Workbook
Resistors in Series
R  R1  R2  R3    
V  V1  V2  V3
IR  IR1  IR2  IR3
R  R1  R2  R3
Resistors in Parallel
1 1
1
1
 

 
R R1 R2 R3
I  I1  I 2  I 3
V V V V
 

R R1 R2 R3
1 1
1
1
 

R R1 R2 R3
A Problem
A Problem
Class Question
What is the potential at points a to e ?
1. Va = 0, Vb = -4 V, Vc = -10 V, Vd = -12 V, Ve = -20 V
2. Va = -20 V, Vb = -16 V, Vc = -10 V, Vd = -8 V, Ve = 0 V
3. Va = 20 V, Vb = 16 V, Vc = 10 V, Vd = 8 V, Ve = 0 V
4. Va = -4 V, Vb = -6 V, Vc = -2 V, Vd = -8 V, Ve = 0 V
5. Va = 4 V, Vb = 6 V, Vc = 2 V, Vd = 8 V, Ve = 0 V
Class Question
What is the potential at points a to e ?
1. Va = 0, Vb = -4 V, Vc = -10 V, Vd = -12 V, Ve = -20 V
2. Va = -20 V, Vb = -16 V, Vc = -10 V, Vd = -8 V, Ve = 0 V
3. Va = 20 V, Vb = 16 V, Vc = 10 V, Vd = 8 V, Ve = 0 V
4. Va = -4 V, Vb = -6 V, Vc = -2 V, Vd = -8 V, Ve = 0 V
5. Va = 4 V, Vb = 6 V, Vc = 2 V, Vd = 8 V, Ve = 0 V
Light light light
Class Question
Rank in order, from
brightest to dimmest, the
identical bulbs A to D.
1. A = B = C = D
2. A > B > C = D
3. A > C > B > D
4. A > C = D > B
5. C = D > B > A
Class Question
Rank in order, from
brightest to dimmest, the
identical bulbs A to D.
1. A = B = C = D
2. A > B > C = D
3. A > C > B > D
4. A > C = D > B
5. C = D > B > A
Another Problem
What is the current in the 600 W resistor?
Student Workbook
Student Workbook
Ground
Student Workbook
Voltage Measurement
To measure the potential difference or voltage across an
element we connect the two voltage leads to the ends of the
element.
Voltage Measurement
What is the effect of connecting a voltmeter (DMM) to an
element?
This is the resistance of
the voltmeter (DMM).
This resistance is more
like 10 MW
If 10 MW and 1kW
1 1 1
   R  999.9W
R R1 R2
Voltage Measurement
What about measuring the voltage of a old battery?
I
V 8.50V

?A
R 17 W
Vemf  Vr  VR  9V  Vr  8.50V
Vr
r
 ?W
I
Current Measurement
To measure the current through
an element we break the circuit
and place the current meter
(DMM) in the circuit so that
current flows through the meter.
Ideal Ammeter

Ideal Ammeter
V
Rs
Rs = 0 for an ideal ammeter
Charging a Capacitor
Kirchhoff’s Rules
Discharging a Capacitors

Write Kirchhoff’s voltage equation for discharging a
capacitor.
Q
 IR   0
C

and
dQ
I
dt
The charge on the capacitor decrease while the charge
through the resistor increases.
dQ
dq

dt
dt
dQ 1

Q0
dt RC


dQ
1

dt
Q
RC
Integrate the equation
Q t 

Q0
t
dQ
1

dt

Q
RC 0

 Q (t ) 
t
ln 



Q
RC
 0 

Q (t )  Q0e

t
RC
Discharging a Capacitor

Write the equation for current and voltage for a
discharging capacitor.
Q(t )  Q0e

t
RC
dQ
I (t ) 
dt


Q0
I (t )  
e
RC

t
RC
 I 0e

t
RC
Use the definition of capacitance and the charge equation
to find the equation for the voltage across the capacitor.
Q
Q
C
or
V
V
Q0
V (t ) 
e
C

t
RC
 V0e

t
RC
Charging a Capacitor

Are the graphs for a
charging capacitor the
same? Discuss this.

Discuss these equations in
your group and make sure
you all understand and can
explain these equations in
terms of the characteristic
of the capacitor.
Charging a Capacitor

Now lets see a charging
capacitor.
For times less than one
time constant
For times greater than a
few time constant
Capacitors in a Circuit

Now lets see what effect a
capacitor has in a circuit?
For times less than one
time constant
For times greater than a
few time constant
Student Workbook
Student Workbook
Student Workbook
Student Workbook