Basic Circuit Analysis – by Colin Brown, Ava Zebzda, Jon Josten and Joseph Hemmingson
Circuit Elements & Variables
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Voltage (Symbol: V| Units: Volts (V) )
o Symbolized by plusses and minuses (+ -)
Current (Symbol: I | Units: Amperes (A))
o Symbolized by arrows ()
Resistance (Symbol: R| Units: Ohms (Ω))
o Symbolized by squiggly lines
Node– Any point you measure on a circuit. Every node has a voltage associated with it.
Wires – Connecting nodes and elements, there is no voltage decrease across a wire
o Elements/Nodes must be connected with wire for current to flow through them
Current flows from high voltage to low voltage, the rate of this flow is proportional to the
difference in voltage between two points (as described by Ohm’s Law).
Ohm’s Law – 𝑉 = 𝐼𝑅 – The equation that relates Voltage, Current, And Resistance.
Basic circuit variables can be thought using water as an analogy:
o Voltage = Pressure
 Increasing pressure increases how much goes through a hose/pipe
o Current = Amount of water flowing in a given time
 Higher pressure or less resistance allow for more water to flow
o Resistance = Reducing the width of the pipe
 If you have kink a hose, the amount of water flowing from it (aka current) will be
reduced
Circuit Elements
 Sources – Objects that provide either voltage or current
 Resistors – Elements that have a set resistance
 Circuit – Elements arranged in a way so that current can flow (i.e. a loop)
Kirchhoff’s Laws
Kirchhoff’s Current Law (KCL) – The total amount of
current going into any node is equal to the amount of
current going out.
(In the picture to the right, i2 + i3 = i1 + i4)
Kirchhoff’s Voltage Law (KVL) – The sum of the
voltages going around any loop in a circuit is zero
(In the picture to the left, V1 + V2 + V3 = VS)
Mesh Current Analysis:
1. Label each mesh of the circuit with a mesh current, going in the clockwise direction.
2. Write KVL equations for each mesh. Each term is a voltage, but will write the terms
using Ohm's law to put them in terms of the mesh currents (V=IR).
3. Solve for the unknown currents using an augmented matrix
Basic Circuit Analysis – by Colin Brown, Ava Zebzda, Jon Josten and Joseph Hemmingson
Color conventions:
= color to denote current
= color to denote voltage
Circuit Practice Problems
Circuit #1
Circuit #3
Circuit #4
Circuit #2