Question

Solve for I 1.

us / nool - usaz - Mosh usz val I (Solve for

Answer 1

Let's solve this problems by two different methods.

a: Knowing that the terminals of resistance R1 are the same as the voltage source of 450V, then they are connected in parallel, which means that both elements has the same voltage in the terminals. Then:

$i=\frac{450}{5}=90A$

b. Applying loop currents, there are 3 loops, where we can get the following equations:

200 ce Z650 T. loov 450v Izstr

$-450-5(I_1-I_2)=0$

$-5(I_2-I_1)-65(I_2-I_3)=0$

$100-20I_3-65(I_3-I_2)=0$

We can describe the circuit with the linear system of equations as

$\begin{bmatrix} -5 & 5 &0 \\ 5 & -70 & 65\\0 & -65 & 85 \end{bmatrix}\begin{bmatrix} I_1\\I_2 \\I_3 \end{bmatrix}=\begin{bmatrix} 450\\0 \\100 \end{bmatrix}\to \begin{bmatrix} I_1\\I_2 \\I_3 \end{bmatrix}=\begin{bmatrix} -114.423\\-24.423 \\-17.5 \end{bmatrix}$

The negaive signs specifyes that the loop currents flows in opposite direction as assumed. Then, current flowing through resitance R1 is:

$i=-114.423+24.423=-90A$

Notice that the magnitude of the current are the same by using both methods. The "advantage" that has the second method is that mathematically you can get the direction of the current, instead of only its magnitud, as method a. Another advantage is that is a more general solution, since it is possible to get other currents of the circuit.