Answer to Question #106258 in Electricity and Magnetism for let me know

Question

[img]https://upload.cc/i1/2020/03/23/lyospF.jpg[/img]


the question is in the picture,R=4

Answer 1

Question

Given the following circuit:

(a) Determine the currents (i₁, i_2, and i₃) in all branches by following the current direction as shown in figure 5.

(b) Hence, find V_ab.

Solution

First, draw the loops:

(a) Write Kirchhoff's voltage law for the given circuit according to the drawn loops and Kirchhoff's current law for node a:

$$i_1-i_2-i_3=0,\\ 5-7=(2+5)i_1+6i_2,\\ 5+10=(2+5)i_1+(3+1)i_3.\\ i_1=0.8723\text{ A},\\ i_2=-1.351\text{ A},\\ i_3=2.223\text{ A}.$$

(b) The voltage between the terminals a and b:

$$V_{ab}=6i_2+7=-1.106\text{ V}.$$