Circuit Analysis
What is Circuit Analysis?
A point in a circuit where two or more components are connected.
Key formula / rule: Ohm's Law
Key points
- To be able to analyze simple DC and AC circuits.
- To apply Kirchhoff's laws and Ohm's law to solve for unknown circuit variables.
- To understand and apply nodal and mesh analysis techniques.
- To utilize network theorems (Superposition, Thevenin, Norton) for circuit simplification.
Common exam trap
Incorrectly applying sign conventions in KVL and KCL.
Definitions
- Term
Node
- Meaning
A point in a circuit where two or more components are connected.
- Term
Branch
- Meaning
A path between two nodes in a circuit.
- Term
Loop
- Meaning
A closed path in a circuit.
- Term
Mesh
- Meaning
A loop that contains no other loops within it.
- Term
Linear Circuit
- Meaning
A circuit where the relationship between voltage and current is linear (obeys superposition and homogeneity).
- Term
Thevenin Equivalent Circuit
- Meaning
A simplified representation of a linear two-terminal circuit consisting of a single voltage source (VTh) in series with a single resistor (RTh).
- Term
Norton Equivalent Circuit
- Meaning
A simplified representation of a linear two-terminal circuit consisting of a single current source (IN) in parallel with a single resistor (RN).
Learning objectives
To be able to analyze simple DC and AC circuits.
To apply Kirchhoff's laws and Ohm's law to solve for unknown circuit variables.
To understand and apply nodal and mesh analysis techniques.
To utilize network theorems (Superposition, Thevenin, Norton) for circuit simplification.
Formulae
- Name
Ohm's Law
- Note
Relates voltage (V), current (I), and resistance (R).
- Expression
V = IR
- Name
Kirchhoff's Current Law (KCL)
- Note
Algebraic sum of currents entering a node is zero.
- Expression
\sumk=1^{n} Ik = 0
- Name
Kirchhoff's Voltage Law (KVL)
- Note
Algebraic sum of voltages around a closed loop is zero.
- Expression
\sumk=1^{n} Vk = 0
- Name
Nodal Analysis
- Note
Requires selecting a reference node.
- Expression
Based on KCL, leads to system of linear equations for node voltages.
- Name
Mesh Analysis
- Note
Requires identifying independent meshes.
- Expression
Based on KVL, leads to system of linear equations for mesh currents.
- Name
Thevenin's Theorem
- Note
Simplifies a linear network to a voltage source in series with a resistance.
- Expression
VTh (open-circuit voltage), RTh (equivalent resistance)
- Name
Norton's Theorem
- Note
Simplifies a linear network to a current source in parallel with a resistance. RN = RTh.
- Expression
IN (short-circuit current), RN (equivalent resistance)
- Name
Superposition Theorem
- Note
Applicable only to linear circuits.
- Expression
Response is sum of responses due to each independent source acting alone.
Prerequisites
Basic algebra and calculus.
Understanding of electrical quantities: voltage, current, resistance, capacitance, inductance.
Familiarity with basic circuit elements.
Common mistakes
Incorrectly applying sign conventions in KVL and KCL.
Confusing voltage and current sources in superposition theorem.
Incorrectly calculating Thevenin/Norton equivalent resistance for circuits with dependent sources.
Assuming linearity for circuits where superposition, Thevenin, or Norton theorems are applied.
Algebraic errors while solving simultaneous equations in nodal or mesh analysis.
Keywords
Ohm's Law
Kirchhoff's Laws
Nodal Analysis
Mesh Analysis
Superposition Theorem
Thevenin's Theorem
Norton's Theorem
Linear Circuits
Voltage Source
Current Source
Resistance
Node
Loop
Mesh
Practice preview
A series RC circuit has R = 10 kOhm and C = 0.1 microF. If a DC voltage of 10 V is applied at t = 0, what is the time constant of the circuit?…
medium
In the circuit shown below, if I1 = 2 A, I2 = 3 A, and I3 = 1 A, what is the value of current I4? (Assume all currents are flowing out of the node.)…
easy
Three resistors with values R1 = 10 Ohm, R2 = 20 Ohm, and R3 = 30 Ohm are connected in parallel. What is the equivalent resistance of the combination?…
easy