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What is the increase in torque expressed as percentage of initial torque, if the current drawnby a dc series motor is increased from 10 A to12 A (neglect saturation )?
- a)21%
- b)25%
- c)41%
- d)44%
Correct answer is option 'D'. Can you explain this answer?
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Given:
Current drawn by the DC series motor (I1) = 10 A
Current drawn by the DC series motor (I2) = 12 A
To find:
Increase in torque expressed as a percentage of initial torque.
Solution:
To calculate the increase in torque, we need to consider the relationship between torque and current in a DC series motor.
In a DC series motor, the torque is directly proportional to the square of the current. Mathematically, it can be represented as:
T ∝ I^2
Where:
T is the torque
I is the current
Step 1: Calculate the initial torque (T1)
Given that the current drawn by the motor is 10 A, we can calculate the initial torque using the above relationship.
T1 = I1^2 = 10^2 = 100
Step 2: Calculate the final torque (T2)
Given that the current drawn by the motor is increased to 12 A, we can calculate the final torque using the same relationship.
T2 = I2^2 = 12^2 = 144
Step 3: Calculate the increase in torque
The increase in torque (ΔT) can be calculated by subtracting the initial torque from the final torque.
ΔT = T2 - T1 = 144 - 100 = 44
Step 4: Calculate the percentage increase
The percentage increase in torque can be calculated by dividing the increase in torque by the initial torque and multiplying by 100.
Percentage increase = (ΔT / T1) * 100 = (44 / 100) * 100 = 44%
Answer:
The increase in torque expressed as a percentage of the initial torque is 44%. Therefore, the correct option is D.
Current drawn by the DC series motor (I1) = 10 A
Current drawn by the DC series motor (I2) = 12 A
To find:
Increase in torque expressed as a percentage of initial torque.
Solution:
To calculate the increase in torque, we need to consider the relationship between torque and current in a DC series motor.
In a DC series motor, the torque is directly proportional to the square of the current. Mathematically, it can be represented as:
T ∝ I^2
Where:
T is the torque
I is the current
Step 1: Calculate the initial torque (T1)
Given that the current drawn by the motor is 10 A, we can calculate the initial torque using the above relationship.
T1 = I1^2 = 10^2 = 100
Step 2: Calculate the final torque (T2)
Given that the current drawn by the motor is increased to 12 A, we can calculate the final torque using the same relationship.
T2 = I2^2 = 12^2 = 144
Step 3: Calculate the increase in torque
The increase in torque (ΔT) can be calculated by subtracting the initial torque from the final torque.
ΔT = T2 - T1 = 144 - 100 = 44
Step 4: Calculate the percentage increase
The percentage increase in torque can be calculated by dividing the increase in torque by the initial torque and multiplying by 100.
Percentage increase = (ΔT / T1) * 100 = (44 / 100) * 100 = 44%
Answer:
The increase in torque expressed as a percentage of the initial torque is 44%. Therefore, the correct option is D.
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Community Answer
What is the increase in torque expressed as percentage of initial torq...
Torque id directly proportion to the square of the current upto saturation ,so torque at 10 amperes is 100 and at 12 ampers is 144 ,so the increase in Torque is about 44 present
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