= Current transformer
{wiki}
A <current transformer> is a <transformer (electrical engineering)> used to reproduce a scaled version of an alternating primary <electric current> in a secondary measurement circuit. Many secondary turns around a primary with few turns make large primary <electric currents> measurable by an instrument. The DOE handbook describes this instrument arrangement and its magnetic operating conditions.<DOE Fundamentals Handbook Electrical Science>[Volume 4, Module 13, Transformer Types, printed p.19, Instrument Current Transformer]{ref}
For ideal magnitudes, primary and secondary turns $N_p,N_s$ give
$$
N_pI_p\simeq N_sI_s,\qquad I_s\simeq\frac{N_p}{N_s}I_p.
$$
The polarity depends on the chosen terminal directions. The <current-transformer burden> is the connected secondary load, including the instrument and connection impedance. With a resistive secondary load $R_b$, $V_s\simeq I_sR_b$ and its dissipated <power> is $I_s^2R_b$.
For an original example, take $N_p=1$, $N_s=200$, primary current $100\,\mathrm A$ RMS, and total secondary <electrical resistance> $R_b=2\,\Omega$. The ideal secondary delivers $0.5\,\mathrm A$, develops $1\,\mathrm V$ and supplies $0.5\,\mathrm{VA}$ to this resistive burden. The reflected primary <electrical resistance> is
$$
R_{\rm reflected}=\left(\frac{N_p}{N_s}\right)^2R_b=50\,\mathrm{\mu\Omega}.
$$
The primary is measured through magnetic coupling, while the secondary still needs a suitable connected circuit.
Real behavior includes <current-transformer ratio error> and <current-transformer phase displacement>. To see why the second matters, let the inferred current magnitude have fractional error $e$ and an extra lag $\delta$ relative to the true current. For a sinusoidal load with lag $\varphi$, the estimated-to-true <active power> ratio is
$$
\frac{\widehat P}{P}=(1+e)\frac{\cos(\varphi+\delta)}{\cos\varphi}
\simeq1+e-\delta\tan\varphi.
$$
With $e=0$, $\varphi=\pi/3$ and $\delta=0.01$ radians, the first-order error is about $-1.73\%$. Correct amplitude scaling alone does not establish correct <power> measurement.
Opening an energized conventional current-transformer secondary removes its normal balancing current and can produce a large induced <electric potential difference>. The DOE handbook specifically explains this open-secondary behavior and its requirement for a closed secondary circuit when the instrument is absent.<DOE Fundamentals Handbook Electrical Science>[Volume 4, Module 13, printed p.19, open-secondary explanation]{ref} A proposed measurement check therefore uses the intended connected burden and compares ratio and phase at relevant <frequencies> and current levels. Core response and saturation limit the ideal scaling model; a conventional inductive <current transformer> does not measure a steady <DC component> by the same transformer action.
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