2024W2 BMEG 220 – Jan 7th 2025
Circuit Elements:
Figure below shows the common circuit elements. Notice the dependant sources.
2024W2 BMEG 220 – Jan 7th 2025
Circuit Topology:
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Node: An electrical connection between two or more elements.
o Ordinary vs. extraordinary vs. super node.
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Branch: Trace between two consecutive nodes with only one element between them.
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Path: Continuous sequence of branches with no node encountered more than once.
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Loop: Closed path with the same start and end node.
o Independent loop
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Mesh: Loop that encloses no other loops.
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In series: Elements that share the same current. They have only ordinary nodes in between.
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In parallel: Elements that share the same voltage. They share two extraordinary nodes.
Kirchhoff’s Voltage Law (KVL):
KVL states that the algebraic sum of all voltages around a closed path (known as a loop) is zero.
𝑀𝑀
� 𝑉𝑉𝑚𝑚 = 0
𝑖𝑖=1
where M is the number of elements in the loop across which there is a potential difference, and
𝑉𝑉𝑚𝑚 is the potential difference across the 𝑚𝑚th element in the loop.
2024W2 BMEG 220 – Jan 7th 2025
Kirchhoff’s Current Law (KCL):
KCL states that the algebraic sum of currents entering a node (or a closed boundary) is zero.
𝑁𝑁
� 𝐼𝐼𝑛𝑛 = 0
𝑖𝑖=1
where 𝑁𝑁 is the number of branches connected to the node and 𝐼𝐼𝑛𝑛 is the current leaving the 𝑛𝑛th node.
Practice problem 1. In the circuit below, obtain 𝑣𝑣1 , 𝑣𝑣2 and 𝑣𝑣3 .
Practice problem 2. In the circuit below, find branch currents 𝐼𝐼1 to 𝐼𝐼4 .
2024W2 BMEG 220 – Jan 7th 2025
Practice Problem 3. In the circuit below, find 𝑣𝑣 and 𝑖𝑖𝑥𝑥 .
Simplifying Resistive circuits:
Usually, we are interested in simplifying part of the resistive circuit, viewed at two chosen ports,
into a single resistor. For resistors in series, we have:
Voltage divider: division of voltage in series resistors:
For resistors in parallel, we have:
Current divider: division of current in parallel resistors:
2024W2 BMEG 220 – Jan 7th 2025
Practice Problem 4: In the circuit below, 𝑖𝑖𝑜𝑜 = 2𝐴𝐴. Find 𝑖𝑖𝑥𝑥 .
Practice Problem 5. In the circuit below, find 𝑣𝑣 and 𝑖𝑖.
Practice Problem 6. In the circuit below, find 𝑅𝑅𝑒𝑒𝑒𝑒 , and 𝑖𝑖𝑜𝑜 .
2024W2 BMEG 220 – Jan 7th 2025
Practice Problem 7. In the circuit below, find 𝑅𝑅𝑎𝑎𝑎𝑎 .