Module 13: Batteries and
Circuit Elements
1
Class 13: Outline
DC Circuits and Kirchhoff’s
Kirchhoff s Loop
Rules
2
Batteries &
Elementary
y Circuits
3
DC Circuits
4
E
Examples
l off Circuits
Ci
it
5
Symbols
y
for Circuit Elements
Battery
Resistor
Capacitor
S it h
Switch
6
Ideal Battery
y
Fixes potential difference between its terminals
Sources as much charge as necessary to do so
Think: Makes a mountain
7
Sign
g Conventions - Battery
y
Moving
g from the negative
g
to p
positive terminal of a
battery increases your potential
ΔV = Vb − Va
Think:
Ski Lift
8
Sign
g Conventions - Resistor
Moving across a resistor in the direction of current
decreases your potential
ΔV = Vb − Va
Think:
Ski Slope
9
Internal Resistance
Real batteries have an internal resistance, r, which is
smallll b
butt non-zero
Terminal voltage:
ΔV = Vb − Va = ε − I r
(Even if you short the leads you don’t
don t get infinite current)
Potential Difference Around a
Cl
Closed
dP
Path
th
Sum of potential differences across all elements
around
d any closed
l
d circuit
i it lloop mustt b
be zero.
r r
ΔV = − ∫ E ⋅ d s = 0
Closed
Path
11
Concept Question: Potential in
Circuits
Where is the potential the highest in the below circuit?
1.
2.
1.
2
2.
3.
4.
2ε
ε
3ε
1
2
3
4
R
3.
4.
12
Series vs
vs. Parallel
Series
Parallel
13
Resistors In Series
The same current I must flow through both resistors
ΔV = I R1 + I R2 = I(R1 + R2 ) = I Req
Req = R1 + R2
14
Resistors In Parallel
Voltage drop across the resistors must be the same
ΔV = ΔV1 = ΔV2 = I1 R1 = I 2 R2 = IReq
ΔV ΔV ΔV
I = I1 + I 2 =
+
=
R1
R2
Req
1
1
1
=
+
Req R1 R2
15
Batteries in Series
ΔV1
ΔV2
Net voltage change is ΔV = ΔV1 + ΔV2
Think: Two Mountains Stacked
16
Batteries in Parallel
Net voltage still ΔV
17
Concept Question Questions:
Two Light
g Bulbs
18
Concept
p Question: Bulbs & Batteries
An ideal
dea batte
battery
y is
s hooked
oo ed to a light
g t
bulb with wires. A second identical
light bulb is connected in parallel to
the first light bulb. After the second
light bulb is connected
connected, the current
from the battery compared to when
only one bulb was connected
connected.
1.
2.
3.
4.
Is Higher
Is Lower
Is The Same
Don’t know
19
Concept Question: Bulbs & Batteries
An ideal battery is hooked to a light
bulb with wires
wires. A second identical
light bulb is connected in series with
th fi
the
firstt lilight
ht b
bulb.
lb Aft
After th
the second
d
light bulb is connected, the current
f
from
the
th battery
b tt
compared
d to
t when
h
only one bulb was connected.
1.
2.
3.
4.
Is Higher
Is Lower
Is The Same
Don’t know
20
MIT OpenCourseWare
http://ocw.mit.edu
8.02SC Physics II: Electricity and Magnetism
Fall 2010
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