You are given an impulse/ Dirac function as follows: 8 (1) = 0.5 u(t) for 0st s 5 a) Determine: b, 8[n] = 0.5 u[n] for 0sns 5 Determine: c) Compare the results from a) and b) and determine whether your computation is right or wrong. If it is wrong, how do you correct it?

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.

Shown in the figure below is an electrical circuit containing three resistors and two batteries. R3 10 R2 R1 Write down the Kirchhoff Junction equation and solve it for I, in terms of I, and Iz. Write the result here: Write down the Kirchhoff Loop equation for a loop that starts at the lower left corner and follows the perimeter of the circuit diagram clockwise. Write down the Kirchhoff Loop equation for a loop that starts at the lower left corner and touches the components R1, R2, and 4V. The resistors in the circuit have the following values: R, = 130 • R2 = 50 R3 = 10 Solve for all the following (some answers may be negative): | Amperes I = I, = Amperes Iz = Amperes NOTE: For the equations, put in resistances and currents SYMBOLICALLY using variables like RR2,R3 and I,,12,13. Use numerical values of 10 and 4 for the voltages.