Circuits II

Exam Preparation Dashboard

A clean visual reference of ten key schematics. Each card shows the circuit diagram, labels, and the core technique to apply.

Problem 1: Nodal Analysis

3 nodes, supernode, dependent voltage source 4ix

2kΩ3mA+\u22124ix1kΩnode 1node 2reference

Use a supernode around the dependent voltage source. Write KCL for the combined node and express the controlling variable in terms of node voltages.

Problem 2: Mesh Analysis

3 meshes, supermesh, dependent current source 2iy

4Ω2Ω6Ω2iy12V+−3Ω5Ωmesh 1mesh 2mesh 3

The dependent current source shared by two meshes creates a supermesh. Write the constraint equation for the source current and solve the system.

Problem 3: Thevenin Equivalent

Resistors, dependent source, terminals a-b

6Ω+\u22123vx12Ω4ΩVs+−ab

Find Vth across terminals a-b and Rth by deactivating independent sources and applying a test source, keeping the dependent source active.

Problem 4: Superposition

10cos(100t) V AC source and 2A DC source

10cos(100t) V+−5Ω2A DC0.1FAC sourceDC source

Solve for the AC and DC contributions separately, then add them. Remember that capacitors block DC in steady state.

Problem 5: Parallel RLC

L, C, R in parallel with a switch

LRCIs

For the natural response, derive the second-order differential equation using KCL and identify damping via α and ω0.

Problem 6: Series RLC

R, L, C in series with a voltage source and switch

Vs+−RLC

Apply KVL around the loop. The response type - overdamped, critically damped, or underdamped - depends on R, L, and C.

Problem 7: s-Domain Transformations

Inductor sL + Li(0−), capacitor 1/sC + v(0−)/s

InductorLi(0\u2212) knowns-domainsL+ Li(0\u2212) \u2212CapacitorCv(0\u2212) knowns-domain1/sC+ v(0\u2212)/s \u2212

Transform each energy-storage element into its s-domain equivalent, including the initial-condition source with correct polarity.

Problem 8: s-Domain Circuit

Resistors, inductor, capacitor in s-domain

Vs(s)+−RsL+\u2212LiL(0\u2212)1/sC+\u2212vC(0\u2212)/s

Redraw the entire network in the s-domain, carry the initial-condition sources through, and solve the algebraic circuit for the desired transform.

Problem 9: Power Factor Correction

R-L load in parallel with a PFC capacitor

RLCVsloadPFC cap

Add a parallel capacitor to offset the lagging reactive power of the inductor. Size C to reach the target power factor angle.

Problem 10: Series Resonance

R, L, C in series with resonant parameters ω0 and Q

Vs cos(ωt)+−RLCω₀ = 1/√(LC)Q = ω₀L/R

At resonance, ω0 = 1 / √(LC). The quality factor Q = ω0L / R sets the bandwidth and the peak voltage across L and C.