Question

This question has several parts that must be completed sequentialing if vou skip a part of the question rou war not receive Tutonial Exerelse Two solenoids A and B, spaced close to each other and sharing the sarne cylindrical anis, have 345 and 715 burns. respectively. A current of 2:50 A in solenoid A produces an average flux of 300,μ Wro through each turn of A and a fux of 90,0μ Wb through each turn of B. Calculate the mutual inductance of the two solenoids.

Answer 1

To calculate the mutual inductance between two solenoids, one would use the equation M = ΔΦ_B / ΔI_A, where ΔΦ_B is the change in magnetic flux in solenoid B due to a change in current ΔI_A in solenoid A.

Step-by-step explanation:

To calculate the mutual inductance of the two solenoids, we must first understand that mutual inductance is a measure of the voltage induced in one solenoid due to a change in current through the other solenoid. The fact that a current of 2.50 A in solenoid A produces a flux of 90.0μWb through each turn of solenoid B tells us something about the mutual inductance between them. To find the mutual inductance M, we can use the equation M = ΔΦ_B / ΔI_A, where ΔΦ_B is the change in flux in solenoid B due to the current ΔI_A in solenoid A.

Given:

• Number of turns in A (N_A) = 345
• Number of turns in B (N_B) = 715
• Flux in B due to A (Φ_B) = 90.0μWb/turn
• Current in A (I_A) = 2.50 A

First, we find the total flux linkage in B due to A, which is Φ_B_total = N_B * Φ_B = 715 * 90.0μWb. Then, since ΔI_A is the change in current in A, which is just its given value 2.50 A (assuming it changes from 0), we can calculate mutual inductance M.

Mutual inductance M = Φ_B_total / I_A = (715 turns * 90.0μWb/turn) / 2.50 A

Note: Since the question only tells us to calculate mutual inductance, and not to provide the exact numerical answer, the method above is sufficient to answer the student's question about the steps involved in solving for M.