2. In the circuit shown below, the switch is closed long enough for the circuit to reach DC steady-state. Then, the switch opens at t = 0. Use the step-by-step method to solve for the current flowing through 1k2 resistor for t> а. Draw the DC steady-state circuit for t = 0-, and determine the current flowing through the inductor, i(-) and the current flowing through the 1kQ resistor i (0-). b. Draw the circuit for t = 0+ and determine the value of i,(0+) using the value of the !3! inductor current at t = 0+. С. Draw the circuit for t = 00 and solve for i,(0)

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Gradient of a Scalar Field

Consider a room or a place where the temperature is denoted by a scalar field T, such that at each point (x, y, z), the temperature is given as T(x, y, z). It is independent of time, in which the temperature rises most quickly. The gradient of T will show the direction at that point by moving away from (x, y, z). How far will the rise in temperature in that direction be determined by the gradient magnitude? Consider a surface that has a height above sea level at point (x, y) which is given by H(x, y). At that point, pointing in the direction of the steepest slope or grade is the gradient of H. The magnitude of the gradient of the vector gives the steepness of the slope at that point. How a scalar field changes in another direction can be measured by the gradient by taking a dot product rather than just the direction of the greatest change?