# Fractional calculus approach to a single loop RL circuit

### Abstract

**ABSTRACT TO BE MODIFIED.**

In a single loop RL circuit, with a DC voltage source, the current is constant. The inductor in a circuit produce a

back emf which creates a reverse current. This back-emf prevents the current in reaching the load hence, there is

no voltage across the load. This reverse current can be described by a first order time dependent differential equation

which shows the gradual increase of reverse current as the magnetic field in the inductor approaches to maximum.

But the theoretical and practical results vary by some degrees due to some systematic errors. To compensate this

error and to determine the numerical result with high precision and accuracy, the equation of reverse current is

solved in fractional differential equation form. This paper focusses on deriving the fractional representation of the

current growth and current decay in a RL Circuit. The authors used the fractional differential equation and fractional

order Laplace transform to derive the solution. Simulation of the equation with varying fractional order is included

in this paper.

*Proceedings of the Samahang Pisika ng Pilipinas*

**38**, SPP-2020-PB-01 (2020). URL: https://paperview.spp-online.org/proceedings/article/view/SPP-2020-PB-01.