Example 10.10 Application: The Current Transformer Although Eqs. (10.55) and (10.56) define the general
transformer, the current transformer is unique in that its primary coil is connected in series with the circuit in which it
operates. In many cases, the primary coil is part of the circuit and the transformer core surrounds it. Three examples of
current transformers are shown in Figure 10.16. The first, in Figure 10.16a, is a simple transformer that, in principle,
can also be used as a voltage transformer. What makes it unique is the low number of turns in the coils, especially in
the primary coil. This is necessary since it is connected in series with the circuit and it should have low impedance. The
transformer in Figure 10.16b is similar except that the primary is a single turn passing through the core. In this case,
the turn ratio a is 1/N2. This particular arrangement is often used because it does not require connections into the circuit
and is particularly useful for measuring purposes (i.e., aI1 ¼ I2). If appropriate, or necessary, the primary may be made
of two or more turns by passing the wire through the core two or more times. A common measuring device based on
this principle is shown in Figure 10.16c. This is a clamping ampere meter. It is essentially a current transformer
without the primary coil. The secondary coil is connected to a measuring device such as a digital meter or bridge. The
core is split and hinged such that it can be opened and closed around the wire in which we wish to measure the current.
With N2 turns in the secondary coil and since the primary in this case has a single turn, the measured current in the
primary is equal to 1/a times the current in the secondary, which is measured directly. The advantage of this device is
that it measures current without the need to cut the circuit, but, as you might expect, it is only accurate at relatively
high currents.
One point of interest with current transformers is that the voltage across the secondary can be very high. For this reason,
the secondary should always be shorted unless a low-impedance load or low-impedance measuring device is connected to
the secondary.
It is required to design a current transformer that will continuously measure a sinusoidal current supplied to an installation
by placing the transformer over one of the wires leading to the installation. The peak current expected is 100 A at 60 Hz.
V or I
a b c