### Transformer

```Transformer
AC Source
 Alternating current comes from generators, not batteries.
• Ideal sinusoidal source
 The symbol for an AC source uses a sine curve.
R
DV
D V AC  V 0 sin  t
I AC 
V0
R
sin  t
Internal Flux
voltage.
DV   N
• Change in voltage to
change in flux
• Change in flux to change in
voltage
D
M
Dt
 The flux can link one
conductor to another.
• Iron for better flux link
• Minimize losses
DVA
R
N
A
NB
Primary Coil
D
M
Dt
 An AC voltage source
produces a changing voltage.
DVA
R
N
NB
A
D
Dt
M

DV A
NA
 The changing voltage creates
an opposing magnetic flux in
the iron.
Secondary Coil
induced voltage in the
second coil.
• Assume all field lines from
primary go through
secondary
 The induced voltage directly
depends on the primary
voltage.
DVA
R
N
NB
A
DVB   N B
D
Dt
M
 NB
DV A
NA
Turns Ratio
 The output voltage depends on
the ratio of the turns in the
coils.
 If NB > NA then the voltage
increases.
• Step-up transformer
 If NB < NA then the voltage
decreases.
• Step-down transformer
DVB 
NB
NA
DV A
Transformers
 Commercial transformers wind
medium.
• Single cylinder of air or iron
• Connecting bar of iron
 The schematic symbol
represents two coils.
 An AC adaptor is an example
of a step-down transformer.
• Convert 120 V AC to 18 V DC
 Power transmission uses step-
up up and step-down
transformers.
• Power plant: 10 kV to 345 kV
• Substation: 345 kV to 7200 V
• Power pole: 7200 V to 120 V
Power Law
 Transformers do not create
power.
• Energy conserved
• Losses small compared to
resistors
 For no power loss, current and
voltage must maintain same
power.
• Current decrease for step-up
• Current increase for stepdown
Pout  Pin
V out I out  V in I in
I out 
V in I in

V out
V in I in
N out
N in
I out 
N in
N out
V in
I in
next
```