To calculate the rotor full torque of the induction motor, we first need to calculate the rotor current.
Given data:
Speed of induction motor (N) = 1400 rpm
Slip speed (Ns) = 100 rpm
Supply voltage (V) = 210 V
Impedance (Z) = 3 + j0.2 Ω
The slip speed is given by the formula:
Ns = (Ns/N) * 100%
Slip speed (S) = Ns/N * 100%
S = 100/1400 * 100
S = 7.14%
The synchronous speed (Nsynchronous) can be calculated using the formula:
Nsynchronous = 120 * f/P
where f is the frequency of the power supply and P is the number of poles of the motor.
Assuming the power supply frequency is 60Hz and the induction motor has 4 poles:
Nsynchronous = 120 * 60 / 4
Nsynchronous = 1800 rpm
Slip (S) = (Nsynchronous - N) / Nsynchronous * 100%
7.14% = (1800 - 1400) / 1800 * 100%
From this equation, we can solve for N:
N = 1400 rpm
Now, we calculate the rotor current (I2) using the formula:
I2 = V / Z
I2 = 210 / (3 + j0.2)
I2 = 210 / (3.2 ∠tan^(-1)(0.2/3))
I2 = 210 / (3.2 ∠3.55°)
I2 = 210 / 3.2
I2 = 65.63 A
Now, we can calculate the rotor full torque (T_e) using the formula:
T_e = (3 * I2^2 * R2) / S
T_e = (3 * 65.63^2 * 3) / 0.0714
T_e = (3 * 4312.87 * 3) / 0.0714
T_e = 38755.83 / 0.0714
T_e = 542460.76 Nm
Therefore, the rotor full torque of the induction motor when the impedance is 3+J0.2 Ω is 542460.76 Nm.
