To solve Example 1.3, we need to apply the Kirchhoff's Voltage Law (KVL) to the two-mesh network shown in Fig. 1.22. Since you referred to a figure and I cannot see it, I will assume a basic two-mesh network with three resistors for explanation purposes. If your circuit has a different configuration, feel free to upload a picture.

Step 1: Define the Mesh Currents

In a two-mesh network, there are two loops (meshes). Let's assign the following:

• Mesh 1 current: $I_1$ (in the clockwise direction)
• Mesh 2 current: $I_2$ (in the clockwise direction)

Step 2: Label the Resistors

Assume the network has three resistances as follows:

• $R_1$ in the first mesh,
• $R_2$ shared by both meshes (between Mesh 1 and Mesh 2),
• $R_3$ in the second mesh.

Additionally, there may be voltage sources $V_1$ in Mesh 1 and $V_2$ in Mesh 2.

Step 3: Express Currents in the Resistors

For each resistor, the current can be expressed based on the mesh currents:

• Current in $R_1$: This resistor is only in Mesh 1, so the current is $I_1$.
• Current in $R_2$: This resistor is shared by both meshes. The current through it is the difference between the two mesh currents, so the current is $I_1 - I_2$.
• Current in $R_3$: This resistor is only in Mesh 2, so the current is $I_2$.

Step 4: Apply Kirchhoff's Voltage Law (KVL)

We now apply KVL to both meshes.

Mesh 1 (Loop 1):

The voltage drops in Mesh 1 are across resistors $R_1$ and $R_2$. By KVL, the sum of voltage drops is equal to the voltage source $V_1$: $V_1 = I_1 R_1 + (I_1 - I_2) R_2$

Mesh 2 (Loop 2):

The voltage drops in Mesh 2 are across resistors $R_2$ and $R_3$. By KVL, the sum of voltage drops is equal to the voltage source $V_2$: $V_2 = (I_2 - I_1) R_2 + I_2 R_3$

Final Equations

The two KVL equations for the system are:

1. $V_1 = I_1 R_1 + (I_1 - I_2) R_2$
2. $V_2 = (I_2 - I_1) R_2 + I_2 R_3$

You can solve these two simultaneous equations to find the values of $I_1$ and $I_2$. Once you have $I_1$ and $I_2$, you can calculate the current through each resistor using the expressions above.

---

If you have any additional information about the circuit (like values for resistances or voltage sources), I can help you solve it fully. Do you want more details or clarifications?

Related Questions:

1. How can Kirchhoff's Current Law (KCL) be applied to the same circuit?
2. What happens if one of the resistors in the two-mesh network is replaced with a capacitor?
3. Can the system be solved using matrix methods instead of solving it by hand?
4. How would the solution change if the current direction in Mesh 2 is counterclockwise?
5. How can superposition be used to simplify solving for currents in this circuit?

Tip:

When writing KVL equations, always ensure that you maintain consistent sign conventions for voltage drops and rises.