Question

A DC generator has flux doubled and speed halved. New EMF is

• A. Doubled
• B. Halved
• C. Same
• D. Zero

Hint:

For proportional relationships in electrical machines, always write down the proportionality formula \(E \propto \Phi N\) to quickly assess changes.
If one factor increases by a certain ratio and another decreases by the same ratio, their product remains unchanged.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks for the effect on the induced electromotive force (EMF) of a DC generator when its magnetic flux is doubled and its rotational speed is halved.
This is a fundamental concept in DC machines where the generated EMF depends on both the field flux and the speed of rotation.

Step 2: Key Formula or Approach:
The induced EMF (\(E_g\)) in a DC generator is given by the formula:
\[ E_g = \frac{\Phi Z N P}{60 A} \]
where:
\(\Phi\) is the flux per pole in Webers,
\(Z\) is the total number of armature conductors,
\(N\) is the speed of rotation in rpm,
\(P\) is the number of poles, and
\(A\) is the number of parallel paths.
Since \(Z, P, A,\) and \(60\) are constant parameters for a given generator, we can write:
\[ E_g \propto \Phi \cdot N \]

Step 3: Detailed Explanation:

• Let the initial flux be \(\Phi_1\) and the initial speed be \(N_1\). The initial induced EMF is \(E_1 \propto \Phi_1 \cdot N_1\).

• According to the problem statement, the flux is doubled, so the new flux is \(\Phi_2 = 2\Phi_1\).

• The speed is halved, so the new speed is \(N_2 = \frac{N_1}{2}\).

• Substituting these new values into the proportional relation gives the new induced EMF (\(E_2\)):
\[ E_2 \propto \Phi_2 \cdot N_2 = (2\Phi_1) \cdot \left(\frac{N_1}{2}\right) \]

• Simplifying the expression:
\[ E_2 \propto \Phi_1 \cdot N_1 \]

• Therefore, the ratio of the new EMF to the initial EMF is:
\[ \frac{E_2}{E_1} = \frac{\Phi_2 N_2}{\Phi_1 N_1} = \frac{(2\Phi_1)\left(\frac{N_1}{2}\right)}{\Phi_1 N_1} = 1 \]

• This shows that the new EMF remains the same as the initial EMF.

Step 4: Final Answer:
The new EMF of the DC generator remains the same.