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DC circuits
Physics Department, New York City College of Technology
Key words Electromotive
force (emf) Terminal voltage Resistors in
parallel and in series
Kirchhoff’s rules Junction rule Loop rule
Capacitors in series and in parallel
RC cuicuits
emf
Electromotive force (emf) refers to the potential difference between the terminals of a source when no current flows out. Its symbol is .
Terminal voltage Terminal voltage is the
potential difference between the terminals of a source when current flows, and is calculated as is the emf r is the internal
resistance of the battery
IrV
Example #1 A 65-Ω resistor is
connected to the terminals of a battery whose emf is 12V and whose internal resistance is 0.5Ω. Calculate (a) the current in the circuit, (b) the terminal voltage of the battery, and (c) the power dissipated in the resistor R and in the battery's internal resistance r.
Example #1—continued
AV
rRI
IrVab
183.05.065
12
, Since
(a)
(b) VAVIrVab 9.11)5.0)(183.0(12
(c)
.02.0)5.0()183.0(
isr in and
,18.2)65()183.0(
is Rin dissipatedpower The
22
22
WARIP
WARIP
r
R
Resistors in series
The equivalent resistance for resistors in series is
...321 RRRReq
Resistors in parallel
The equivalent resistance for resistors in parallel is ...
1111
321
RRRReq
Voltage drop along wire
Disc 18, #1 Disc 18, #2 Disc 18, #6
Series/parallel resistors
Disc 17, #23 Disc 17, #24
Example #2
Two 100Ω resistors are connected (a) in parallel, and (b) in series, to a 24V battery. What is the current through each resistor and what is the equivalent resistance of each circuit?
Example #2—continued
(a)
21
so resistor,each through
flow tosplitsbattery thefrom Icurrent totalThe
III
AIII
AV
R
VIA
V
R
VI
48.0
24.0100
24,24.0
100
24
21
22
11
50 so
,50
1
100
2
100
1
100
11
eq
eq
R
R
Example #2—continued
(b)
AV
RR
VI
RRIIRIRV
VVV
12.0100100
24
)(
and resistors,both in same theis I
21
2121
21
200or
,20012.0
0.24
21 RRRA
V
I
VR
eq
eq
Kirchhoff’s rules The junction rule: at any junction point,
the sum of all currents entering the junction must equal the sum of all currents leaving the junction. It is based on the conservation of electric charge.
The loop rule: the sum of the changes in potential around any closed path of a circuit must be zero. It is based on the conservation of energy.
Example #3
Calculate the currents I1, I2, and I3.
Example #3—continued
(a) .
a,point at rulejunction sKirchhoff'Apply
213 III
(b) .0414530
loop,upper the torule loop sKirchhoff'Apply
31 II
(c) .080)120(30
loop,outer the torule loop sKirchhoff'Apply
21 II
Example #3—continued
(d) 1.4I3.821
30I80I
get we(c), Eq. From
11
2
(e) I73.01.141
30I45I
get we(b), Eq. From
11
3
Example #3—continued
AI
AI
AI
IIIII
7.1
6.2
87.0
.4.18.373.01.1
(a), Eq. into (e) and (d) Substitute
3
2
1
11231
Capacitors in series and in parallel
The equivalent capacitance for capacitors in series is
The equivalent capacitance for capacitors in parallel is
...1111
321
CCCCeq
...321 CCCCeq
RC circuits In the charging
process,
In the discharging process,
The time constant is
Switch
C
R
ε
)1( / RCtc eV
RCtc eVV /
0
RC
RC charging curve
Disc 18, #28
