Question

which of the following relationships about a coil are true? check all that apply. which of the following relationships about a coil are true?check all that apply. the induced emf is proportional to the resistance of the coil. the induced emf is proportional to the time derivative of the current in the coil. the induced emf is proportional to the self-inductance of the coil. the induced emf is proportional to the current in the coil.

Answer 1

The induced emf in a coil is proportional to the rate of change of magnetic flux and the number of turns in the coil, and it follows Faraday's and Lenz's laws.

Step-by-step explanation:

According to Faraday's Law of Induction, the induced electromotive force (emf) in a coil is directly proportional to the rate of change of magnetic flux through the coil. This law can be mathematically expressed as E = -N (∆Φ/∆t), where E is the induced emf, N is the number of turns in the coil, and ∆Φ/∆t is the rate of change of magnetic flux. Two important concepts related to this are self-inductance and Lenz's Law. Self-inductance is the property of a coil where a change in current induces an emf within the same coil, opposing the change according to Lenz's Law. Thus, in a circuit with inductance, the induced emf is proportional to the rate of change of current, as well as to the self-inductance of the coil itself, which depends on its geometry and the number of turns (N).

Answer 2

The induced emf is proportional to the self-inductance and time derivative of the current in a coil, and directly proportional to the number of coils, but not related to the square of the number of coils or resistance.

Step-by-step explanation:

When examining the relationships about a coil and induced electromotive force (emf), we can apply Faraday's and Lenz's Law to determine which statements are true. Induced emf is not proportional to the resistance of the coil, but it is in fact proportional to the self-inductance of the coil and the rate of change of magnetic flux with respect to time. Therefore, the induced emf is proportional to the time derivative of the current in the coil. Additionally, the induced emf is directly proportional to the number of turns in the coil and this suggests that neither of the statements about being inversely or directly proportional to the square of the number of coils is correct. The induced emf is actually proportional to the number of coils, but not to the square of this number.