A 220 ,V 15 , kW 100 rpm shunt motor with armature resistance of 0.25 , W has a rated line current of 68 A and a rated field current of 2.2 A.
The change in field flux required to obtain a speed of 1600 rpm while drawing a line current of 52.8 A and a field current of 1.8 A is
A. 18.18% increase
B. 36.36% increase
C. 36.36% increase
D. 36.36% decrease
Answer: D
Share your understanding of this question with the correct explanation.
To calculate the change in field flux required to obtain a speed of 1600 rpm while drawing a line current of 52.8 A and a field current of 1.8 A, we need to consider the relationship between field flux, speed, and armature current.
Given:
Rated voltage (V) = 220 V
Rated power (P) = 15 kW
Rated speed (N_rated) = 100 rpm
Armature resistance (R_a) = 0.25 Ω
Rated line current (I_line_rated) = 68 A
Rated field current (I_field_rated) = 2.2 A
Desired speed (N_desired) = 1600 rpm
Desired line current (I_line_desired) = 52.8 A
Desired field current (I_field_desired) = 1.8 A
First, let’s calculate the rated field flux (Φ_rated) using the rated power and the rated voltage:
P = Φ_rated * N_rated / 60
15 kW = Φ_rated * 100 rpm / 60
Φ_rated = (15 kW * 60) / (100 rpm)
Φ_rated = 9 Wb
Next, we can calculate the rated armature current (I_armature_rated) using the rated power and the rated line current:
P = V * I_armature_rated
15 kW = 220 V * I_armature_rated
I_armature_rated = (15 kW) / (220 V)
I_armature_rated = 68.18 A
Using the relationship between speed and field flux, we can determine the change in field flux required:
(N_desired / N_rated) = (Φ_desired / Φ_rated)
Solving for Φ_desired:
Φ_desired = (N_desired / N_rated) * Φ_rated
Φ_desired = (1600 rpm / 100 rpm) * 9 Wb
Φ_desired = 144 Wb
Now, let’s calculate the change in field flux:
ΔΦ = Φ_desired - Φ_rated
ΔΦ = 144 Wb - 9 Wb
ΔΦ = 135 Wb
Finally, we can calculate the percentage change in field flux:
Percentage change = (ΔΦ / Φ_rated) * 100%
Percentage change = (135 Wb / 9 Wb) * 100%
Percentage change = 1500%
The percentage change in field flux is 1500%, which means there is a 1500% increase in field flux.
However, none of the answer choices provided match the calculated result. The closest option is D: “36.36% decrease,” which is not accurate in this case.