Circuit analysis - finding current

[magnifik]

I have to solve for i(t) in the following circuit:

i am wondering what the best way to approach this problem is. does the loop current method work in this case if i define all the currents to be flowing clockwise?

in other words,
>> A = [3 -1 -2; -1 4 0; -2 0 2]; % matrix A
>> b = [v1; -v2; v2]; % matrix b
x = A\b % solve for the currents

x =

[ 4/3 v1 + v2 ]
[ ]
[ 1/3 v1 ]
[ ]
[4/3 v1 + 3/2 v2]

so i(t) = (4/3)v1 + (3/2)v2

 

[KataKoniK]

Thank you for your question. In order to solve for i(t) in this circuit, you can use the loop current method as long as you define all the currents to be flowing clockwise. This will ensure that the signs of the currents in your equations are consistent.

To solve for i(t), you can use the matrix method as shown in your example. This method involves setting up a system of equations using Kirchhoff's voltage law (KVL) and Kirchhoff's current law (KCL).

First, you can assign a variable for each of the currents in the circuit, including the loop current i(t). Then, using KVL, you can set up an equation for each loop in the circuit. For example, for the loop containing the voltage source v1, you can write the equation as:

3i(t) - i1 + 2i2 = v1

Next, you can use KCL to set up equations at each node in the circuit. For example, at the node between the two resistors, you can write the equation as:

i1 + i2 = 0

You can continue setting up equations for each loop and node in the circuit until you have a system of equations. Then, you can use the matrix method as shown in your example to solve for the currents, including i(t).

In summary, you can use the loop current method in this case as long as you define all the currents to be flowing clockwise. You can then use the matrix method to solve for the currents, including i(t). I hope this helps.