A six pole generotar with fixed field excitation developes an e.m.f. of `100 V` when operating at `1500` r.p.m. At what speed must it rotate to develop `120 V`?

Options

A. 1200 rpm
B. 1800 rpm
C. 1500 rpm
D. 400 rpm

Answer

To solve the problem step by step, follow these instructions:

### Step 1: Understand the relationship between EMF and speed
The EMF (E) generated by a generator is directly proportional to the speed of rotation (ω) when the field excitation is fixed. This can be expressed as:
\[ E \propto \omega \]
This means that if we know the EMF at one speed, we can find the EMF at another speed using the ratio of the two speeds.

### Step 2: Set up the equations for the two scenarios
For the first scenario:
- EMF \( E_1 = 100 \) V
- Speed \( \omega_1 = 1500 \) RPM

For the second scenario:
- EMF \( E_2 = 120 \) V
- Speed \( \omega_2 = ? \) (this is what we need to find)

### Step 3: Write the proportionality equation
From the relationship established in Step 1, we can write:
\[ \frac{E_1}{E_2} = \frac{\omega_1}{\omega_2} \]

### Step 4: Substitute the known values into the equation
Substituting the known values into the equation gives:
\[ \frac{100}{120} = \frac{1500}{\omega_2} \]

### Step 5: Cross-multiply to solve for \( \omega_2 \)
Cross-multiplying gives:
\[ 100 \cdot \omega_2 = 120 \cdot 1500 \]

### Step 6: Calculate \( \omega_2 \)
Now, solve for \( \omega_2 \):
\[ \omega_2 = \frac{120 \cdot 1500}{100} \]

### Step 7: Simplify the calculation
Calculating the right side:
\[ \omega_2 = \frac{120 \cdot 1500}{100} = 120 \cdot 15 = 1800 \text{ RPM} \]

### Conclusion
The speed at which the generator must rotate to develop an EMF of 120 V is \( \omega_2 = 1800 \) RPM.