# CP2 Circuit Theory Revision lecture

Electronics - Devices

Oct 5, 2013 (4 years and 9 months ago)

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CP2 Circuit Theory

Revision Lecture

Basics,
Kirchoff’s

laws,
Thevenin

and Norton’s
theorem, Capacitors, Inductors

June 2004 q7

September 2010 q7

AC
theory, complex notation, LCR circuits

September 2005 q8

June 2002 q7

Op
-
amps

Sam Henry (Tony Weidberg
) www.physics.ox.ac.uk/users/weidberg/teaching

V
0

I

R
1

R
2

R
3

V
0

IR
1

IR
2

IR
3
=0

+

+

+

+

V
0

+IR
1

+IR
2

+IR
1

I
1

I
3

I
2

I
4

I
1
+I
2

I
3

I
4
=0

Kirchoff’s laws

V
eq

R
eq

R
eq

Thevenin

and Norton theorem

In Practice, to find V
eq
, R
eq

R
L


(open circuit) I
L

0 V
eq
=V
L

R
L

0 (short circuit) V
L

0

R
eq
= resistance between terminals
when all voltages sources shorted

Capacitors

C

+Q

-
Q

Q = CV

Capacitors resist change in voltage

Capacitors in series

Capacitors in parallel

Stored energy

stored in form of electric field

C
1

C
2

C
N

Inductors

Inductors in series

Inductors in parallel

Stored energy

stored in form of magnetic field

L

“back
emf”

Self
-
inductance

Inductors resist a
change of current

L
1

L
2

+

V
0

R

+

V
0

R

L

C

RC and RL circuits

CP2 June 2004

Check

Energy conservation:

Total energy dissipated
by resistor = Energy
delivered by source

CP2 September 2010

AC circuit theory

Voltage represented by complex exponential

Impedance relates current and voltage V=ZI

in complex notation:

Resistance

R

Inductance

j

L

Capacitance

1/j

C

and combinations thereof

Impedance has magnitude and phase

represented by real component of

easily shown from

Q=VC

Current is given by

So |Z| gives the ratio of magnitudes of V and I, and

give the
phase difference by which current lags voltage

CP2 September 2005

The complex impedance is given by the voltage in a circuit
divided by the current when both are expressed in complex
form. The magnitude of the complex impedance is the ratio
of the magnitudes of the voltage and current; the phase is
the phase lag between the voltage and current.

Physics 3 June 2002

An oscillating voltage of frequency
ω
, V(t)=V
0
cos(
ω
t) is represented
in complex notation by V
0
e
j
ω
t
. The current in the circuit is then given
by I=V/Z, where Z is the complex impedance Z=|Z|
e
j
φ
, where |Z| is
the ratio of the magnitude of the voltage to the magnitude of the
current, and
φ

is the phase by which the current leads the voltage.
The real component of Z is the resistance, and the imaginary
component is the reactance

where C the capacitance and
L is the inductance of the circuit. Complex impedances allow circuits
when inductance and capacitance to be analysed using linear circuit
theory in the same way as resistance

The sum of these peak voltages
is not equal to V
0

as V
R
, V
C

and
V
L
all have different phases.
When the complex voltages are
summed V
R
+V
C
+V
L
=V
0

LCR circuit

overdamped solution

critically damped solution

underdamped (oscillatory) solution

+

V
0

R

C

L

I(t)

Op
-
amps

Gain is very large (A

)

Inputs draw no current (Z
IN
=

)

Feedback

v
+
=v

V
OUT

+

v
+

v

V
IN

R
1

R
2

Non
-
Inverting
Amplifier Circuit

+

V
OUT

V
IN

R
1

Inverting Amplifier Circuit

R
2

v

v
+

i

i