ENSC2003 - Lecture 4

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ENSC2003 - Lecture 3
Kirchhoff’s Laws - Slides

Kirchhoff’s Current Law (KCL)

• If $N$ conductors connect to a node, then at this particular node, the sum of input and output currents is zero
  ${\sum }_{n=1}^N{i}_n=0$
• Convention:
  • Current flowing into node is positive
  • Current flowing out of node is negative

Kirchhoff’s Voltage Law (KVL)

• The sum of voltages around a closed loop is zero
  $\sum V=0$
• Convention:
  • Voltage rises ($-$ -> $+$) have positive sign
  • Voltage drops ($+$ -> $-$) have negative sign

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Systematic Approaches - Slides

Systematic Approaches

• Two approaches covered:
  • Node-to-datum analysis
  • Mesh analysis

Node-To-Datum (NTD) Analysis

• We describe a voltage at each node using a reference voltage
  • This reference is known as a node-to-datum voltage
• Each node is described having a difference in potential compared to the node-to-datum voltage

Steps for NTD:

1. Identify all nodes in a circuit and select node as reference node, voltage at reference node is assumed to be -> $0$
2. If a voltage source is connected between reference node and non-reference node -> nodal voltage = voltage from voltage source
3. Apply KCL to remaining non-reference nodes + use Ohm’s Law to express unknown branch currents in terms of node voltages
4. Solve resulting simultaneous equations to obtain unknown node voltages

Resistors are passive elements, that means if a current moves across a resistor with resistance of $5$ Ohms and moves from node A to node B, node A is considered the ($+$) end and node B is the ($-$) end:
$I=\frac{V_A-V_B}{5}$

If a voltage source is connected between two non-reference nodes, you cannot use NTD to solve circuit -> you must use supernode analysis (covered next lecture)

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ENSC2003 - Lecture 5