Question

Shin 3 2 (20 pts) Use nodal analysis to find V, in the circuit belotw 40 V ( 20Ω 16 2 ao 0 10 10 10 60v A- n a-40 v 醫. : 60

Just wanna check if its right?

Answer 1

It's absolutely right but let me show you step by step solution.

From the diagram

$I_x=\frac{V_a}{20}$                                                                 ....(1)

Applying nodal analysis at node 'a'

$\frac{40-V_a}{20}+\frac{V_b-V_a}{10}-I_x=0$

$\frac{40-V_a}{20}+\frac{V_b-V_a}{10}-\frac{V_a}{20}=0$                                   ....from (1)

$2+\frac{V_b}{10}-\frac{V_a}{5}=0$

Multiplying by 10 on both sides, we have

$20+V_b-2V_a=0$

$\Rightarrow 2V_a-V_b=20$                                       ....(2)

Applying nodal analysis at node 'b'

$\frac{V_a-V_b}{10}-\frac{V_b}{10}+4I_x=0$

$\frac{V_a-V_b}{10}-\frac{V_b}{10}+\frac{V_a}{5}=0$                                ....from (1)

$\frac{3V_a}{10}-\frac{V_b}{5}=0$

Multiplying by 10 on both sides, we have

$3V_a-2V_b=0$                                        ....(3)

On multiplying equation (2) by 2 on both sides, we have

$4V_a-2V_b=40$

Subtracting equation (3) from it, we have

$(4V_a-2V_b)-(3V_a-2V_b)=40$

$4V_a-2V_b-3V_a+2V_b=40$

$V_a=40\;V$

Putting it in equation (3), we have

$(3\times 40)-2V_b=0$

$120-2V_b=0$

$\Rightarrow V_b=60\;V$

From the diagram

${\color{Red} V_o=V_b=60\;V}$

Now, from equation (1)

$I_x=\frac{V_a}{20}$

$I_x=\frac{40}{20}$

$I_x=2\;A$