D.C motor run of 120 V . If armature current at `e_(b)` = 115 V is 10 A . Then find out current just after motor is started :

Options

A. 240 A
B. 230 A
C. 120 A
D. 400 A

Answer

To solve the problem step by step, we will follow the reasoning and calculations outlined in the video transcript.

### Step 1: Understand the Given Information
We have a DC motor running at an applied voltage of \( V = 120 \, \text{V} \). The back EMF (\( E_b \)) when the armature current is \( I = 10 \, \text{A} \) is given as \( E_b = 115 \, \text{V} \).

### Step 2: Write the Equation for the Motor
The voltage equation for the DC motor can be expressed as:
\[ V = E_b + I \cdot R \]
Where:
- \( V \) is the applied voltage,
- \( E_b \) is the back EMF,
- \( I \) is the current,
- \( R \) is the armature resistance.

### Step 3: Substitute the Known Values
We can substitute the known values into the equation:
\[ 120 = 115 + 10 \cdot R \]

### Step 4: Solve for Resistance \( R \)
Rearranging the equation to solve for \( R \):
\[ 10 \cdot R = 120 - 115 \]
\[ 10 \cdot R = 5 \]
\[ R = \frac{5}{10} = 0.5 \, \Omega \]

### Step 5: Determine the Current Just After the Motor Starts
At the moment the motor starts (at \( t = 0 \)), the back EMF (\( E_b \)) is zero because the motor has not yet begun to rotate. Thus, the voltage equation simplifies to:
\[ V = I \cdot R \]

### Step 6: Substitute the Values to Find the Current
Now substituting the values for \( V \) and \( R \):
\[ 120 = I \cdot 0.5 \]

### Step 7: Solve for Current \( I \)
Rearranging to solve for \( I \):
\[ I = \frac{120}{0.5} = 240 \, \text{A} \]

### Final Answer
The current just after the motor is started is \( 240 \, \text{A} \).

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