Given Rx= 5 ohm , I0=4A , Va=15V ,X=10 and Y =95 Find a ,b , c and d Given: R, Ia, V., X, Y.Use nodal analysis to set up equations for node 1 and node 2 respectively in the formavı + bvz = X,cv1 + dvz = Y.The node voltage of node 1 is denoted by v and the node voltage of node 2 is denoted by v2.Calculate the unknown coefficients a, b, c and d.R,I.voVa2R.5vo

Answered: Given Rx= 5 ohm , I0=4A , Va=15V ,X=10…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Question

Given R_x= 5 ohm , I₀=4A , V_a=15V ,X=10 and Y =95

Find a ,b , c and d

Given: R, Ia, V., X, Y.
Use nodal analysis to set up equations for node 1 and node 2 respectively in the form
avı + bvz = X,
cv1 + dvz = Y.
The node voltage of node 1 is denoted by v and the node voltage of node 2 is denoted by v2.
Calculate the unknown coefficients a, b, c and d.
R,
I.
vo
Va
2R.
5vo

Expert Solution

Step 1

According to question:

Applying Nodal analysis at node 1, this will give

$∵ \frac{V_{a} - v_{1}}{R_{x}} = \frac{v_{1}}{2 R_{x}} + \frac{v_{1} - v_{2}}{R_{x}} + I_{0} \Rightarrow 2 V_{a} - 2 v_{1} = v_{1} + 2 v_{1} - 2 v_{2} + 2 I_{0} R_{x} \Rightarrow 2 V_{a} - 2 I_{0} R_{x} = 5 v_{1} - 2 v_{2} \Rightarrow - 5 v_{1} + 2 v_{2} = 2 I_{0} R_{x} - 2 V_{a} ∵ X = 2 I_{0} R_{x} - 2 V_{a} = 2 \times 4 \times 5 - 2 \times 15 = 10 V ∴ a v_{1} + b v_{2} = X On comparision, \Rightarrow a = - 5 \Rightarrow b = 2$