ib 9V 402 Vo ia B No. Total Values 01 Total Voltage 02 Total Current 03 Total Resistance No. Resistance Voltage Current 04 6Ω 05 40 N 06 60 Ω

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Q: Determine Vo using 1) Nodal Analysis 2) Mesh Analy= 4A 20 60 40 Vo 3V Ž40 2A

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Q: 3. Determine Vo using mesh analysis. 20V 45 V 1502 M Il 82 + F% + 14 1022 12 3222 M 13 2012 +48V

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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?