Neglecting saturation, if the current taken by DC series motor is increased from 10A to 12A, percentage increase in the torque will be

Explanation:

DC Series Motor Torque Calculation:

Definition: The torque (T) produced by a DC series motor is directly proportional to the square of the armature current (I_a) under normal operating conditions, where magnetic saturation is neglected. Mathematically, this relationship can be expressed as:

T ∝ I_a²

This means that any change in the armature current will result in a corresponding change in the torque, following a quadratic relationship.

Given Data:

• Initial current, I_a1 = 10 A
• Final current, I_a2 = 12 A

Objective: To calculate the percentage increase in torque when the current increases from 10 A to 12 A.

Step-by-Step Solution:

1. Expression for torque: Since torque is proportional to the square of the armature current, we can write:

T₁ ∝ I_a1² and T₂ ∝ I_a2²

2. Ratio of torques: To find the percentage increase in torque, calculate the ratio of the final torque (T₂) to the initial torque (T₁):

T₂/T₁ = (I_a2/I_a1)²

Substituting the given values of I_a1 and I_a2:

T₂/T₁ = (12/10)²

T₂/T₁ = (1.2)² = 1.44

3. Percentage increase in torque: The percentage increase in torque is given by:

Percentage Increase = [(T₂ - T₁)/T₁] × 100

Substituting T₂/T₁ = 1.44:

Percentage Increase = [(1.44 - 1) × 100] = 0.44 × 100 = 44%

Thus, the percentage increase in torque is 44%.

Hence the current Option 1 is (0.44 or 44%)