Question

Can any one help me please

Answer 1

Vc = 60[v], I = 5[amp]; Vx = 20 [v]

Step-by-step explanation:

To solve this problem we have to perform a mesh analysis, we identify the meshes of the circuit we can appreciate that they are two meshes, in each we suppose a direction of current and we make a sum of voltages equal to zero for each mesh. Remember that ohm's voltage by law is defined as the product of current by resistance.

In the attached image, you can see the direction of the supposed current in each of the meshes, from this analysis we obtain two equations with the I & i2 currents

Mesh 1

`60+(6*i)-(6*i_(2))+8*i = 0\\60+(14*i)-(6*i_(2))=0`

Mesh 2

`(12*i_(2)) + (6*i_(2))-(6*i)=0\\(18*i_(2))-(6*i)=0\\(18*i_(2))=(6*i)\\i = 3*i_(2)`

Now we can find the current i, replacing in the first equation.

`60+(14*3*i_(2))-(6*i_(2))=0\\-60= (42-6)*i_(2)\\i_(2) = - 1.66666[amp]\\`

and

i = 3* (-1.66666)

i = -5 [amp]

Note: The negative sign means that the current has the opposite direction to the supposed originally.

Therefore:

Vc = 60 [v]

io = 5 [amp]

Now to determine the current in the resistance of 6 [ohms], we must know the current that passes through it, by means of a summation of currents in any of its nodes.

This current is equal to:

-1.66 = I + (-5)

I = 3.33[amp]

And using the ohm's law we can find the voltage

Vx = (3.33*6)

Vx = 20 [V]