The figure shows two resistors in parallel, with values R1 and R2. The current I, divides between them somehow: 4 +I2 = I0 R1 Io I1 12 R2 (a) Determine the total power dissipated by the circuit as a function of I1, R1, 2, and R2. Your expression should depend on I, and I, but these variables are not independent. Use the constraint that the total current is I, to rewrite your expression for the power as a function of I, and I1. (b) Apply the principle of minimum power dissipation to your expression for the power. That is, minimize the total power with respect to I1, then find the currents I, and Iz that flow through the resistors. Show that this gives the same currents as the standard circuit formula for a "current divider". This illustrates a general variational principle that holds for all direct current networks: The distribution of currents within the network, for given input current I, is always that which gives the least total power dissipation.

The figure shows two resistors in parallel, with values R1 and R2. The current I, divides between them somehow: 4 +I2 = I0 R1 Io I1 12 R2 (a) Determine the total power dissipated by the circuit as a function of I1, R1, 2, and R2. Your expression should depend on I, and I, but these variables are not independent. Use the constraint that the total current is I, to rewrite your expression for the power as a function of I, and I1. (b) Apply the principle of minimum power dissipation to your expression for the power. That is, minimize the total power with respect to I1, then find the currents I, and Iz that flow through the resistors. Show that this gives the same currents as the standard circuit formula for a "current divider". This illustrates a general variational principle that holds for all direct current networks: The distribution of currents within the network, for given input current I, is always that which gives the least total power dissipation.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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