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Chapter 2 of 8

AC Fundamentals and Resistor Networks

Electrical current comes in two principal forms. Direct current (DC) flows steadily in one constant direction and is the type produced by batteries. Alternating current (AC) periodically reverses direction, typically in a sinusoidal pattern, and is the form delivered by power grids. In the United States, household AC operates at 60 Hz (cycles per second), while in Europe and many other regions the standard is 50 Hz.

Because AC voltage varies with time, it is characterized by several related quantities. The peak voltage is the maximum instantaneous value, while the root-mean-square (RMS) value represents the equivalent DC voltage that would deliver the same average power to a resistive load. For a sine wave, \(V_{rms} = V_{peak}/\sqrt{2} \approx 0.707 \times V_{peak}\). Conversely, a standard 120 V RMS household supply corresponds to a peak voltage of \(120 \times \sqrt{2} \approx 169.7\) V.

Resistors are the simplest passive components, and they combine predictably in circuits. In series, resistances add directly: \(R_{total} = R_1 + R_2 + R_3 + \dots\). In parallel, the reciprocals add: \(1/R_{total} = 1/R_1 + 1/R_2 + 1/R_3 + \dots\). A common resistor network, the voltage divider, exploits these rules by placing two resistors in series across an input voltage and tapping the output across one of them, yielding \(V_{out} = V_{in} \times R_2 / (R_1 + R_2)\). This simple configuration provides a convenient way to scale a voltage down to any desired fraction of the input.

All chapters
  1. 1Foundational Laws: Ohm's Law, Power, and Kirchhoff's Laws
  2. 2AC Fundamentals and Resistor Networks
  3. 3Energy Storage Components: Capacitors and Inductors
  4. 4Transient Response and Resonance
  5. 5Active Components: Transistors and Operational Amplifiers
  6. 6Digital Electronics: Logic Gates, Memory, and Converters
  7. 7Power Systems, Transformers, and Power Quality
  8. 8Signals, Filters, Electromagnetics, and Circuit Theorems

Drill it

Reading is not remembering. These come from the Electrical Engineering Fundamentals deck:

Q

What is Ohm's law?

Ohm's law states that V = IR, where V is voltage (volts), I is current (amps), and R is resistance (ohms).

Q

How do you calculate current using Ohm's law?

I = V / R. Current equals voltage divided by resistance.

Q

How do you calculate resistance using Ohm's law?

R = V / I. Resistance equals voltage divided by current.

Q

What is the unit of electrical resistance?

The ohm (Ω), named after Georg Simon Ohm.