Given below are two statements as Assertion (A) and Reason (R )
Assertion (A): Two identical loops, one of copper and another of aluminium are rotated with the same speed in the same magnetic field. The emf induced in both the loop will be same .
Reason (R ):The magnitude of induced emf is directly proportional to the rate of change of magnetic flux linked with the circuit.

Options

A. Both A and R are true and R is also the correct explanation of A.
B. Both A and R are true but R is not the correct explanation of A.
C. A is true but R is false.
D. A is false and R is also false.

Answer

To solve the question, we need to analyze the given Assertion (A) and Reason (R) statements.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that two identical loops, one made of copper and the other of aluminum, are rotated with the same speed in the same magnetic field. The induced emf in both loops will be the same.
- Since the loops are identical in size and shape, and they are subjected to the same magnetic field and rotational speed, we can conclude that the conditions for inducing emf are identical for both loops.

2. **Understanding the Reason (R)**:
- The reason states that the magnitude of induced emf is directly proportional to the rate of change of magnetic flux linked with the circuit.
- This is a fundamental principle of electromagnetic induction, as described by Faraday's Law. The induced emf (E) can be expressed as:
\[ E = -\frac{d\Phi}{dt} \]
- Here, \(\Phi\) is the magnetic flux, and the negative sign indicates the direction of the induced emf as per Lenz's Law.

3. **Calculating Induced EMF**:
- For both loops, the induced emf can be calculated using the formula derived from Faraday's Law:
\[ E = \frac{1}{2} B \omega R^2 \]
- Where:
- \(B\) = magnetic field strength,
- \(\omega\) = angular speed of rotation,
- \(R\) = radius of the loop.
- Since both loops are identical and are rotating in the same magnetic field with the same angular speed, the induced emf in both loops will be:
\[ E_{copper} = E_{aluminum} = \frac{1}{2} B \omega R^2 \]

4. **Conclusion**:
- Since the induced emf in both loops is equal, the assertion (A) is correct.
- The reason (R) is also correct as it accurately describes the principle behind the induced emf.
- Additionally, the reason explains why the assertion is true, as it relates to the principle of electromagnetic induction.

### Final Answer:
Both the Assertion (A) and Reason (R) are correct, and the reason explains the assertion.