WOLFRAM|DEMONSTRATIONS PROJECT

AC Transformers

​
simplified
load R, L
N
P
(turns)
10
N
S
(turns)
5
V
P
(rms volts)
10
i
P
(rms amps)
5
AC frequency (Hz)
60
R (ohms)
50
L
S
(henries)
0.5
An electrical transformer is a device to change the voltage and amperage of alternating currents. In the simple design shown here,
N
P
primary wire coils (blue) and
N
S
secondary coils (red) are wound around a ferromagnetic core. An alternating current in the primary circuit creates a time-dependent magnetic field in the core, which, in turn, induces an alternating current in the secondary circuit, via Faraday's law of electromagnetic induction. The respective rms voltages are in the same ratio as the numbers of turns:
V
S
/
V
P
=
N
S
/
N
P
. If
N
S
<
N
P
, this acts as a step-down transformer. Long-distance transmission lines use high voltage and low currents to minimize energy losses. A sequence of step-down transformers then reduces the voltage to household levels (120 volts in the U.S.). If the secondary resistance and induction are negligibly small (simplified model), the primary and secondary currents are given by the reciprocal relation
i
P
/
i
S
=
N
S
/
N
P
.
If the load resistance
R
and inductance
L
S
are taken into account, the secondary current is affected by the impedance of the circuit. Details of the magnitude of
i
S
are omitted in this elementary discussion, except to note that the secondary voltage and current are no longer in phase, the current leading the voltage by the phase angle
​
arctan(2πf
L
s
/R)
.