A Rogowski coil is a device for measuring alternating current (AC) or high speed current pulses. It is a coil of wire which is shown in figure. For measuring the current flow through any conductor, the rogowski coil is then covered around that conductor. It acts just like a current transformer , but there is no iron core.
When current flows through the conductor, then some voltage produces in the rogowski coil. This voltage is directly proportion to the rate of change of current in the conductor. That means, induced voltage increases when the current flow increases and induced voltage decreases when the current flow decreases. An electronic integrator circuit is connected to the output of this the Rogowski coil to obtain that voltage. This integrator circuit is basically analog to digital converter which is often used for this purpose. And the output digital signal is used for current measuring purpose.