Question

By using Kirchhoff's Laws, it can be shown that the currents I1, I2, and I3 that pass through the three branches of the circuit in the figure satisfy the given linear system. Solve the system to find I1, I2, and I3. (Round your answers to three decimal places.)

I(sub)1 + I(sub)2 − I3 = 0
8I(sub)1 − 4I(sub)2 = 2
4I(sub)2 + 2I(sub)3 = 8
R = 8, R2 = 4, R3 = 2
V = 2, V(sub)2 = 8 ...?

Answer 1

By applying Kirchhoff's junction and loop rules, we can formulate and solve a system of equations to find the unknown currents I1, I2, and I3 in a complex circuit.

Step-by-step explanation:

To solve for the currents I1, I2, and I3 using Kirchhoff's Laws, we need to apply Kirchhoff's junction rule and loop rules to obtain three independent equations that represent the relationship between the currents, resistances, and electromotive forces (EMFs) in the circuit.

Applying Kirchhoff's junction rule at point A, we obtain:

I1 = I2 + I3

Next, we apply Kirchhoff's loop rule to the upper loop and the lower loop of the circuit to get two additional equations:

Upper loop: 8I1 - 4I2 = 2

Lower loop: 4I2 + 2I3 = 8

With these three equations, we can now solve for the three unknown currents I1, I2, and I3. This process involves substitution and elimination to isolate each variable and compute their values.

Answer 2

Solve the second equation for I_1 and the third equation for I_3. Then plug those into the first equation. From here you can solve for I_2. Then you can plug that in to equation 2 to solve for I_1. Then plug in to equation 3 to solve for I_3.