Given values:

P = 4
f = 50 Hz
N = 1455 RPM
E1Line = 415 V
Turn Ratio K = Rotor turns/Stator turns = 1/2 = 0.5

We know that the synchronous speed of an induction motor with P poles and f frequency is given by:

Ns = 120f/P

Substituting the given values, we get:

Ns = 120 x 50/4 = 1500 RPM

The slip of an induction motor is given by:

s = (Ns - Nr)/Ns

where Nr is the rotor speed. We can calculate the slip as follows:

s = (1500 - 1455)/1500 = 0.03

The frequency of the rotor emf in running condition is given by:

fr = sf

where f is the supply frequency. Substituting the values, we get:

fr = 0.03 x 50 = 1.5 Hz

At standstill, the induction motor acts as a transformer, and the ratio of the rotor to stator turns is given by K = 0.5. Using the formula for transformer emf ratio, we get:

E2ph/E1ph = K

where

E1ph is the stator emf per phase in volts
E2ph is the rotor induced emf per phase at standstill.

Since the motor is star-connected, we can find the stator emf per phase as follows:

E1ph = E1Line/sqrt(3) = 415/sqrt(3) = 239.6 volts

Substituting the values, we get:

E2ph/E1ph = 0.5
E2ph = 0.5 x 239.6 = 119.8 volts

The induced emf is proportional to the slip

E2r = sE2

Substituting the values, we get:

E2r = 0.03 x 119.8 = 3.594 volts

Therefore, the answers are:

(i) The frequency of the rotor emf in running condition is 1.5 Hz.
(ii) The induced emf in the rotor at standstill is 119.8 volts.
(iii) The induced emf in the rotor under running conditions is 3.594 volts.