Is electric current reference frame dependent? $$EMF=\frac{dW_{external}}{dq}$$
$$dW_{ext}=\vec{F}_{net}.d\vec{s}$$
$$\vec{F}_{net}=\vec{F}_{inertial}+\vec{F}_{non-inertial}$$
$$dW_{inertial}+dW_{non-inertial}=dW_{external}$$
After reading the mathematical equations above,I think the emf of a battery acting as a source must depend on the reference frame{inertial and non inertial}. It means if emf is a reference dependent quantity then electric current produced in the circuit must also depend on reference frame we choose. Can we conclude that electric current is also a reference dependent quantity?
 A: 
Can we conclude that electric current is also a reference dependent quantity?

yes. Electric current density forms part of a four-vector whose timelike component is the electric charge density, in the same way that momentum forms the spacelike part of a four-vector whose timelike component is energy.
In other words, $j^\mu = (\rho,\vec j)$ is a four-vector and transforms as such under Lorentz frame transformations. Among other things, this entails that


*

*the charge density mixes into the current, i.e. a stationary charge produces an electric current when seen from a reference frame where the charge is moving (a fact which is not at all surprising, but)

*if a neutral configuration with nonzero currents is seen from an appropriate reference frame, then a net charge density will appear.


This last bit is pretty surprising, and it is not expected from classical kinematics: a stationary test charge won't feel a force from a neutral set of currents, but a moving test charge will feel a force (which, by continuity, must be proportional to the velocity, at least at low $v$). Or, in other words, it sees a magnetic field.
For more details on that connection, I recommend the relativity chapters at the start of Ed Purcell's Electricity and Magnetism.
A: Yes, the current is RF-dependent quantity. The charge density $\rho$ and the current flux $\vec{j}$ are RF-dependent quantities - they form a four-vector $j_{\mu}$.
In particular, if you take a neutral piece of a wire with a constant current $I$, then in a moving RF it will be charged, with the charge density absolute value and its sign RF dependent: $\rho'\ne 0$.
