**7.B] What is a slip of an induction motor and derive an expression for the frequency of rotor current in terms of supply frequency?**

**Answer:**

**Slip of Induction Motor**:

Slip of the induction motor is defined as the difference between the** synchronous speed (Ns)** and **actual speed of rotor i.e. motor (N)** expressed as a fraction of the synchronous speed (N.).

This is also called **absolute slip or fractional slip and is denoted as ‟s‟**.

The percentage slip is expressed as,

**Expression for Rotor frequency (f _{r})**

In case of induction motor, the speed of rotating magnetic field in stator is,

Wkt the slip of Induction motor

where, **N **– is the speed of Rotor in rpm

At start of motor , when N = 0, the slip s = 1 and stationary rotor has maximum relative motion with respect to rotating magnetic field. Hence maximum EMF gets induced in the rotor at start.

The frequency of this induced EMF at start is same as motor actually it rotates with speed N , the relative speed of rotor with respect R.M.F decreases and becomes equal to slip speed of** Ns – N**.

The induced EMF in rotor depends on rate of cutting flux i.e. relative speed **Ns- N**. Hence in running condition magnitude of induced EMF decreases so as its frequency.

If **‘f _{r}’ **is the frequency of rotor induced EMF and rotor currents,

In running condition at slip speed Ns – N then there exists a fixed relation between (Ns- N), f

_{r}, and P.

So we can write for rotor in running condition,