# INC 111 Basic Circuit Analysis Week 3 Nodal Analysis.

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INC 111 Basic Circuit Analysis Week 3 Nodal Analysis

Systematic Methods for Analyzing a Circuit Nodal Analysis Mesh Analysis (Loop analysis)

Node Node = Point that connected together on the same wire V Example 3 nodes

Nodal Analysis Procedure 1. Count the number of nodes = N 2. Choose one of the nodes to be a reference node (0V) when there is no ground 3. Give the voltage for other nodes to be V1, V2, V3, … 4. Use Kirchoff’s current law on each node to form N-1 equations 5. Solve the equations to find V1, V2, V3, …

Example 0V (reference) V1 V2

0V (reference) V1 V2 Equation 1

0V (reference) V1 V2 Equation 2

Solve the Equations V1 V2 V1 = 5 V V2 = 2.5V

Example V1 V2 V3 0V

V1 V2 V3 0V Equation 1

V1 V2 V3 0V Equation 2

V1 V2 V3 0V Equation 3

Solve the Equations

Cramer’s Rule (Optional)

Supernode When there is a voltage source in the circuit, direct KCL cannot be used because we do not know the current in the voltage source. We will use the idea of supernode. Supernode is the method that combines 2 nodes together when using KCL. It will include the voltage source within the circle when using KCL.

Example V1 V2 V3 0V

V1 V2 V3 0V Equation 1

V1 V2 V3 0V Equation 2 supernode Equation 3

V1 = -4.952 V V2 = 14.333 V V3 = 13.333 V

Example 0V V1 V2

Sanwa YX360TRF Multimeter

Resistance Measurement Read this Range Select these ranges

Voltage Measurement Read this Range Select these ranges

Current Measurement Read this Range Select these ranges

Measure the Resistance of Ammeter and Voltmeter Adjust a multimeter to measure volt and use another multimeter to measure its resistance. Adjust a multimeter to measure amp and use another multimeter to measure its resistance.

Resistor Code

Standard Resistor Value 1R010R100R1K010K100K1M010M 1R212R120R1K212K120K1M2n/a 1R515R150R1K515K150K1M5n/a 1R818R180R1K818K180K1M8n/a 2R222R220R2K222K220K2M2n/a 2R727R270R2K727K270K2M7n/a 3R333R330R3K333K330K3M3n/a 3R939R390R3K939K390K3M9n/a 4R747R470R4K747K470K4M7n/a 5R656R560R5K656K560K5M6n/a 6R868R680R6K868K680K6M8n/a 8R282R820R8K282K820K8M2n/a E12 -Standard

Protoboard