The armature of a `DC` motor has `20Omega` resistance. It draws a current of `1.5 A` when run by `200 V DC` supply The value of back emf induced in it will be

Options

A. 150 V
B. 170 V
C. 180 V
D. 190V

Explanation

To find the back EMF (Electromotive Force) induced in a DC motor, we can use the relationship between the supply voltage, the current flowing through the motor, and the resistance of the motor's armature.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Resistance of the armature, \( R = 20 \, \Omega \)
- Current drawn by the motor, \( I = 1.5 \, A \)
- Supply voltage, \( V = 200 \, V \)

2. **Use Ohm's Law to Find the Voltage Drop Across the Armature:**
The voltage drop across the armature can be calculated using Ohm's Law:
\[ V_R = I \times R \]
Substituting the values:
\[ V_R = 1.5 \, A \times 20 \, \Omega = 30 \, V \]

3. **Relate the Supply Voltage, Back EMF, and Voltage Drop:**
The relationship between the supply voltage \( V \), back EMF \( E \), and the voltage drop \( V_R \) across the armature is given by:
\[ V = E + V_R \]
Rearranging this equation to find the back EMF \( E \):
\[ E = V - V_R \]

4. **Substitute the Values to Find Back EMF:**
Now substitute the known values into the equation:
\[ E = 200 \, V - 30 \, V = 170 \, V \]

5. **Conclusion:**
The value of the back EMF induced in the motor is:
\[ E = 170 \, V \]

### Final Answer:
The back EMF induced in the DC motor is **170 V**.

---