# Concept of Rogowski Coil and its Working

**What is Rogowski Coil?**

Rogowski Coil is an electrical device used for the measurement of alternating (AC) current. It can measure high speed transient current, pulsed current as well as power frequency AC current. It is simply a toroidal coil named after German physicist Walter Rogowski.

A Rogowski coil is evenly wound coil on a non-magnetic former. This non-megnatic former is either plastic or other flexible material. The wiring wound is made in such a way that the end point is brought to the starting point along the central axis of the former. This is shown in figure below.

In the above figure, the starting point of coil is A and end point is B. The winding wire B is brought to starting point A through the central axis up to point C. Thus the two terminal A and C of the coil are at the same side. These terminals are connected to electronic Intergrator Circuit to get output voltage proportional to the current.

**Working Principle of Rogowski Coil **

The working of Rogowski Coil is based on Faraday’s Law of Electromagnetic Induction. This coil surrounds the conductor whose current is to be measured. Since any current carrying conductor creates magnetic field in its surrounding, this field links with the Rogowski Coil. Due to this linkage, an emf is induced in the coil whose magnitude Is proportional to the rate of change of current in the conductor.

v = Ldi/dt where L is the inductance of coil.

Since inductance of coil is given as

L = μ_{0}AN/l

Where A = Cross-sectional area of coil = πr^{2}

l = 2πr = Length of coil

N = Number of turns in the coil

μ_{0 }= Magnetic permeability of air

= 2πx10^{-7} A-m

To obtain output voltage proportional to the conductor current, an electronic Integrator Circuit is connected across the Rogowski coil terminals. Therefore the output voltage is given as

V_{0} = ∫Ldi/dt

= (μ_{0}AN/l)I + C

where C is constant of integration.

Usually this constant of integration is made zero by design, therefore

**V _{0} = (μ_{0}AN/l)I**

**Advantage of Rogowski Coil**

- It is very simple to use. Since it is not closed loop as the second terminal is brought back to the starting point, it is quite flexible and can easily be wrapped around any conductor whose current is to be measured.
- Since it is wrapped on nonmagnetic former, its inductance is quite low. Due to this, it can respond to fast changing current.
- As it has no iron core to saturate, its response to current is very linear when subjected to high current. This is an added advantage.

**Disadvantage of Rogowski Coil**

The main disadvantage of this device is that, it requires electronic integrator circuit for current replication. This integrator posse looses.