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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### 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
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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