cp2 circuit theory - university of oxford · 2019. 11. 11. · stored energy, rc, rl and lcr...
TRANSCRIPT
CP2 Circuit TheoryRob Smith [email protected]
https://www2.physics.ox.ac.uk/contacts/people/robertsmith (‘Teaching’ tab):
• Problem set
• Synopsis and reading list
• Lecture summaries
• Slides
But do make your own notes because: (i) it is helpful for you to learn, (ii) I will say extra things, (iii) I will do some stuff on the blackboard.
Thanks to Todd Huffman
Why study circuit theory?
• Foundations of electronics: analogue circuits, digital circuits, computing, communications…
• Scientific instruments: readout, measurement, data acquisition…
• Physics of electrical circuits, electromagnetism, transmission lines, particle accelerators, thunderstorms…
• Not just electrical systems, also thermal, pneumatic, hydraulic circuits, vacuum, control theory
Aims of this course:Understand basic circuit components (resistors, capacitors, inductors, voltage and current sources, op-amps)
Analyse and design simple linear circuits (considering both DC, AC and transient response)
+
– +
+
Circuit Theory: Synopsis
• Basics: voltage, current, Ohm’s law, ideal voltage and current sources…
• Kirchoff’s laws and tricks for solving: mesh currents, node voltage, Thevenin and Norton’s theorem, superposition…
• Capacitors:
• Inductors:
• AC theory: complex notation, phasor diagrams, RC, RL, LCR circuits, resonance, bridges…
• Op amps: ideal operational amplifier circuits…
Stored energy, RC, RL and LCR transient circuits.
Mathematics required
• Differential equations
• Complex numbers
• Linear equations
0ILC
1
dt
dI
L
R
dt
Id2
2
V(t)=V0ejωt
jXRZ Z
VI
V0–I1R1–(I1–I2)R3 = 0
(I1–I2)R3–I2R2+2 = 0
Covered by Complex Nos & ODEs / Vectors & Matrices lectures
Charge, voltage, current, power
Potential difference: V=VB–VA
Energy to move unit charge from A to B in electric field
B
AV dsE VE
B
AQW dsE
Charge: determines strength of electromagnetic forcequantised: e=1.602×10-19C [coulombs]
[volts]
Power: work done per unit time
nAvedt
dQI
No. electrons/unit vol
Cross-section area of conductor
Drift velocity
Charge Q=e
Current: rate of flow of charge
[amps]
[watts = J/s]
P =dW
dt=d QV
dt= IV
Ohm’s law
Voltage difference current
I
L
AV
A
LR
IRV
R=Resistance Ω[ohms]
ρ=Resistivity Ωm
Resistor symbols:
R
Resistivities
Silver 1.6×10-8 Ωm
Copper 1.7×10-8 Ωm
Manganese 144×10-8 Ωm
Distilled water 5.0×103 Ωm
PTFE (Teflon) ~1019 Ωm
R
1g Conductance
[seimens]conductivity[seimens/m]
1
Power dissipation by resistor:R
VRIIVP
22
Voltage source
V0
Ideal voltage source: supplies V0
independent of currentRload
+–
+–
V0
Symbol: or
V0 +
Constant current source
Ideal current source: supplies I0 amps independent of voltage
RloadI0
Symbol: or
Circuits
Out of these components we can make (arbitrarily complicated) circuits:
But how do we work out what they do…
Kirchoff’s Laws
I Kirchoff’s current law: Sum of all currents at a node is zero
I1
I3
I2
I4
I1+I2–I3–I4=0
0In
(conservation of charge)
It does not matter whether you pick “entering”or “leaving” currents as positive.
BUT keep the same convention for all currents on one node!
KCL
II Kirchoff’s voltage law: Around a closed loop the net change of potential is zero(Conservation of Energy)
V0
I
R1
R2
R3
0Vn
But what about the signs of Vn?
KVL
Passive Sign Convention
IRV
V0 + Sources have a + sign on the terminal the current normally leaves
Where do we put the + sign on a resistor (or other passive component)?
Procedure
• Choose direction of current you are defining as positive.
• For any passive component make a + sign on the side of that component that the current is entering.
• When applying KVL, as you go round a loop a – to + component has a negative voltage and a + to –component has a positive voltage.
Learn it; Live it; Love it!
Passive Sign Convention
The ‘convention’ is related to how power input/output from a circuit is defined:
• Power flowing out of a circuit into an electrical component is defined as positive.
• Power flowing into a circuit from an electrical component is defined as negative.
𝐼𝑛𝑉𝑛 = 0Power conservation
II Kirchoff’s voltage law: Around a closed loop the net change of potential is zero(Conservation of Energy)
V0
I
R1
R2
R3
0Vn
5V
2kΩ
2kΩ
Calculate the voltage across R2
1kΩ
Show on blackboard
Passive Sign Convention
IRV
V0 + Sources have a + sign on the terminal the current normally leaves
Where do we put the + sign on a resistor (or other passive component)?
Procedure
• Choose direction of current you are defining as positive.
• For any passive component make a + sign on the side of that component that the current is entering.
• When applying KVL, as you go round a loop a – to + component has a negative voltage and a + to –component has a positive voltage.
Learn it; Live it; Love it!
Kirchoff’s voltage law:
V0
I 1kW
2kW
2kW
-V0+IR1+IR2+IR3=0
0Vn
+
+
+
+
–
–
–
–
–V0
+IR1
+IR2
+IR3
5V=I(1+2+2)kΩ
VR2=1mA×2kΩ=2V
I=1mA
Series / parallel circuits
Show on blackboard
Series / parallel circuits
R1 R2 R3
Resistors in series: RTotal=R1+R2+R3…
n
nT RR
R1 R2 R3
Resistors in parallel
321
n nT
R
1
R
1
R
1
R
1
R
1
Two parallel resistors: 21
21T
RR
RRR
Potential divider
R1
R2
V0
21
20
RR
RV
USE PASSIVE SIGN CONVENTION!!!
Show on blackboard
Voltage source
V0
Ideal voltage source: supplies V0
independent of current
Real voltage source:
Rload
V0Rint
Rload
+–
𝑉load = 𝑉0 ×𝑅𝑙𝑜𝑎𝑑
𝑅load + 𝑅int
𝑉load = 𝑉0 − 𝐼𝑅int
Constant current source
Ideal current source: supplies I0 amps independent of voltage
Real current source:
RloadI0
RloadRintI0
Symbol: or
𝐼load = 𝐼0 −𝑉
𝑅int
𝐼load = 𝐼0 ×𝑅int
𝑅load + 𝑅int
End of Lecture 1