8. A motors draws 2 A of current when running at full speed and connected to a 120 Volt line. Suppose the same motor is connected to a 220 Volt power source and as the result it runs 1.4 times faster than its full speed and draws 9 A. What is the armature resistance of the motor?
8. A motors draws 2 A of current when running at full speed and connected to a 120 Volt line. Suppose the same motor is connected to a 220 Volt power source and as the result it runs 1.4 times faster than its full speed and draws 9 A. What is the armature resistance of the motor?
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Transcribed Image Text:### Motor Armature Resistance Calculation
A motor draws 2 A of current when running at full speed and connected to a 120 Volt line. Suppose the same motor is connected to a 220 Volt power source and as a result it runs 1.4 times faster than its full speed and draws 9 A. What is the armature resistance of the motor?
**Options:**
A. 7.4 Ohms
B. 8.4 Ohms
C. 9.4 Ohms
D. 10.4 Ohms
E. 11.4 Ohms
---
**Explanation:**
To calculate the armature resistance (\( R_A \)) of the motor, the following information can be used based on the motor's operational data:
1. **At 120V and 2A:**
- Voltage ( \( V_1 \) ) = 120V
- Current ( \( I_1 \) ) = 2A
- Motor runs at full speed ( \( n_1 \) )
2. **At 220V and 9A with 1.4 times Speed:**
- Voltage ( \( V_2 \) ) = 220V
- Current ( \( I_2 \) ) = 9A
- Motor runs at speed \( n_2 \) which is 1.4 times of \( n_1 \) ( \( n_2 = 1.4n_1 \) )
Using these, we can set up the equations and solve for the armature resistance.
---
In an educational setting, this calculation involves understanding the relationship between voltage, current, speed, and resistance in an electrical motor. Follow the steps to determine the resistance:
1. **Back EMF Relation**: The back electromotive force (EMF) in the motor is proportional to its speed. If the speed increases by a factor of 1.4:
- \( E_2 = 1.4 \cdot E_1 \)
2. **Ohm's Law Application**:
- For first condition: \( V_1 = E_1 + I_1 \cdot R_A \)
- For second condition: \( V_2 = E_2 + I_2 \cdot R_A \)
3. **Solving the Equations:**
Substitute \( E_2
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