Determine the current in 4 ohm resistance of the circuit shown 6 AA 10 V 10Ω 3Ω www 24 V 3.1 A O 4.1 A O 5.1 A O 6.1 A

An electric toothbrush has a base designed to hold the toothbrush handle when not in use. As shown, the handle has a cylindrical hole that fits loosely over a matching cylinder on the base. When the handle is placed on the base, a changing current in a solenoid inside the base cylinder induces a current in a coil inside the handle. This induced current charges the battery in the handle. We can model the base as a solenoid of length ℓ with NB turns (as shown), carrying a current i, and having a cross-sectional area A. The handle coil contains NH turns and completely surrounds the base coil. Find the mutual inductance of the system.

Although we are given the restrictions on Kd and Kp, explain how we arrived at that conclusion and show all work necessary to arrive at the given solution for each restriction.