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Statement-1 : The induced e.m.f. and cur...

Statement-1 : The induced e.m.f. and current will be same in two identical loops of copper and aluminium, when rotated with same speed in the same magnetic field.
Statement-2 : Induced e.m.f. is proportional to rate of change of magnetic field while induced current depends on resistance of wire.

A

If both Assertion and Reason are corrent and Reason is the corrent explanation of Assertion.

B

If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

C

If Assertion is true but Reason is false.

D

If Assertion is false but Reason is ture.

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The correct Answer is:
To solve the problem, we need to analyze both statements given in the question. ### Step 1: Analyze Statement 1 **Statement 1**: The induced e.m.f. and current will be the same in two identical loops of copper and aluminium, when rotated with the same speed in the same magnetic field. - Both loops are made of different materials (copper and aluminum), which have different resistivities. - The induced e.m.f. (electromotive force) in a loop rotating in a magnetic field is given by the formula: \[ \text{Induced e.m.f.} = B \cdot \omega \cdot A \] where \(B\) is the magnetic field strength, \(\omega\) is the angular velocity, and \(A\) is the area of the loop. - Since both loops are identical and rotating in the same magnetic field at the same speed, the induced e.m.f. will be the same for both loops. ### Conclusion for Statement 1 - The induced e.m.f. is the same, but the current induced in each loop depends on the resistance of the material. - The resistance \(R\) of a wire is given by: \[ R = \rho \cdot \frac{L}{A} \] where \(\rho\) is the resistivity, \(L\) is the length, and \(A\) is the cross-sectional area. - Since the resistivities of copper and aluminum are different, the resistances of the loops will also be different. - Therefore, the induced current, given by \(I = \frac{\text{Induced e.m.f.}}{R}\), will not be the same for both loops. ### Step 2: Analyze Statement 2 **Statement 2**: Induced e.m.f. is proportional to the rate of change of magnetic field while induced current depends on the resistance of the wire. - According to Faraday's law of electromagnetic induction, the induced e.m.f. is proportional to the rate of change of magnetic flux, which is related to the rate of change of the magnetic field. - The induced current, as established earlier, is indeed dependent on the resistance of the wire, which varies based on the material. ### Conclusion for Statement 2 - Both parts of Statement 2 are correct: the induced e.m.f. is proportional to the rate of change of the magnetic field, and the induced current depends on the resistance of the wire. ### Final Conclusion - **Statement 1 is incorrect** because while the induced e.m.f. is the same, the induced currents are different due to different resistances. - **Statement 2 is correct**. ### Answer - Therefore, the correct answer is that Statement 1 is false and Statement 2 is true.

To solve the problem, we need to analyze both statements given in the question. ### Step 1: Analyze Statement 1 **Statement 1**: The induced e.m.f. and current will be the same in two identical loops of copper and aluminium, when rotated with the same speed in the same magnetic field. - Both loops are made of different materials (copper and aluminum), which have different resistivities. - The induced e.m.f. (electromotive force) in a loop rotating in a magnetic field is given by the formula: \[ ...
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