Circuit Theory #16 | Mesh-Current Examples - Equivalent Resistance + Dependent Source

Instructor: Dr. Süleyman Burak ÇELİK

Sixteenth lesson in the Circuit Theory series. This lesson continues the mesh-current method with two worked examples. Main ideas: - Apply a test source to find equivalent resistance - Choose clockwise mesh currents and write KVL equations - Use difference terms for shared resistors - Keep the controlling-current relation visible when a dependent source is present - Return from mesh currents to the requested circuit quantity Worked example 2: - Goal: equivalent resistance seen from terminals a and b - Test source: 12 V - Resistors: five 10 ohm resistors - Mesh equations give `i1 = 1.2 A`, `i2 = 0.6 A`, `i3 = 0.6 A` - Result: `R_eq = 12 / 1.2 = 10 ohm` Worked example 3: - Independent source: 50 V - Dependent source: `15 i_x` - Controlling current: `i_x = i1 - i3` - Mesh-current results: `i1 = 29.6 A`, `i2 = 26 A`, `i3 = 28 A` - Result: `i_x = 29.6 - 28 = 1.6 A` downward Main takeaway: - Mesh analysis stays systematic even when the goal is not a mesh current - A test source turns equivalent resistance into `R_eq = V_test / I_test` - For dependent sources, first express the controlling variable in terms of mesh currents