Question

A dc generator running at 30 rev/s generates an e.m.f. of 200 V. Determine the percentage increase in the flux per pole required to generate 250 V at 20 rev/s.

• A. 87.5%
• B. 85.5%
• C. 75.5%
• D. 70.5%

Hint:

In DC machines, emf varies directly with both speed and magnetic flux. Any reduction in speed must be compensated by an increase in flux.

Answer 1

The Correct Option is A

Step 1: Write the emf equation of a DC generator.
For a DC generator, the generated emf is directly proportional to flux per pole and speed.
\[ E \propto \Phi N \]
Step 2: Form the ratio of emfs under two operating conditions.
\[ \frac{E_2}{E_1} = \frac{\Phi_2 N_2}{\Phi_1 N_1} \]
Step 3: Substitute the given values.
\[ \frac{250}{200} = \frac{\Phi_2 \times 20}{\Phi_1 \times 30} \]
Step 4: Simplify the equation.
\[ 1.25 = \frac{2}{3} \times \frac{\Phi_2}{\Phi_1} \]
\[ \frac{\Phi_2}{\Phi_1} = 1.875 \]
Step 5: Calculate percentage increase in flux.
\[ \text{Percentage increase} = (1.875 - 1) \times 100 = 87.5% \]
Step 6: Conclusion.
The flux per pole must be increased by
\[ \boxed{87.5%} \]