Introductory Circuits
Circuits is the most self-contained unit in the course -- Ohm's law and the series/parallel combination rules don't depend on anything from the mechanics units before it. The core skill is reducing a combination circuit down to a single equivalent resistance step by step, then working back outward to find the current and voltage at every individual resistor, which is the same reduce-then-expand pattern the final two lessons apply to full combination circuits and power.
What you'll learn
- Apply Ohm's law to relate voltage, current, and resistance.
- Analyze series circuits (total resistance, current, voltage drops).
- Analyze parallel circuits (total resistance, branch currents, voltage).
- Analyze combination (series-parallel) circuits by stepwise simplification.
- Calculate electrical power dissipated by a resistor.
- Apply Kirchhoff's laws (simply) to verify circuit analysis.
- Interpret circuit diagrams and identify series vs. parallel connections.
1. Current, Voltage, Resistance, and Ohm's Law
Current \(I\) is the rate of charge flow through a conductor; voltage \(V\) is the energy provided per unit charge; resistance \(R\) is a material's opposition to current flow. For an ohmic resistor, these relate through Ohm's law: \(V = IR\).
2. Series Circuits
In a series circuit, there is only one path for current, so the same current flows through every component: \(I_1 = I_2 = \cdots\). Voltage divides across the components in proportion to their resistance, and the total resistance is the simple sum: \(R_{series} = R_1 + R_2 + \cdots\).
3. Parallel Circuits
In a parallel circuit, each branch has the same voltage across it (both ends of every branch connect to the same two nodes), while the current splits among the branches: \(I_{total} = I_1 + I_2 + \cdots\). Equivalent resistance is found from \(\dfrac{1}{R_{parallel}} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \cdots\), and is always *less* than the smallest individual resistor — adding a parallel path always gives current an easier route, lowering overall resistance.
4. Combination Circuits
Most real circuits mix series and parallel sections. Solve by simplifying step by step: identify a sub-group that is purely series or purely parallel, collapse it into a single equivalent resistance, and repeat until only one resistance remains. Then work backward — find the total current first, then use it to find voltages and currents for each simplified stage, all the way back to the original individual resistors.
5. Electrical Power
Electrical power dissipated by a resistor (or delivered by a source) can be written three equivalent ways: \(P = IV = I^2R = \dfrac{V^2}{R}\). Which form is fastest depends on which two quantities you already know.
Key equations
- V = IR — Any basic Ohm's law problem
- Rseries = R1 + R2 + ... — Total resistance in series
- 1/Rparallel = 1/R1 + 1/R2 + ... — Total resistance in parallel
- P = IV = I^2R = V^2/R — Power dissipation
- I same through series elements; V same across parallel branches — Analyzing combination circuits