$$\require{cancel}$$

# 10: Direct-Current Circuits

In the preceding few chapters, we discussed electric components, including capacitors, resistors, and diodes. In this chapter, we use these electric components in circuits. A circuit is a collection of electrical components connected to accomplish a specific task. The second section of this chapter covers the analysis of series and parallel circuits that consist of resistors. Later in this chapter, we introduce the basic equations and techniques to analyze any circuit, including those that are not reducible through simplifying parallel and series elements. But first, we need to understand how to power a circuit.

• 10.1: Prelude to Direct-Current Circuits
An amplifier circuit takes a small-amplitude signal and amplifies it to power the speakers in earbuds. Although the circuit looks complex, it actually consists of a set of series, parallel, and series-parallel circuits.
• 10.2: Electromotive Force
All voltage sources have two fundamental parts: a source of electrical energy that has a electromotive force (emf) and an internal resistance r. The emf is the work done per charge to keep the potential difference of a source constant. The emf is equal to the potential difference across the terminals when no current is flowing. The internal resistance r of a voltage source affects the output voltage when a current flows. The voltage output of a device is called its terminal voltage.
• 10.3: Resistors in Series and Parallel
Basically, a resistor limits the flow of charge in a circuit and is an ohmic device where V=IR. Most circuits have more than one resistor. If several resistors are connected together and connected to a battery, the current supplied by the battery depends on the equivalent resistance of the circuit.
• 10.4: Kirchhoff's Rules
Kirchhoff’s rules can be used to analyze any circuit, simple or complex. The simpler series and parallel connection rules are special cases of Kirchhoff’s rules. Kirchhoff’s first rule, also known as the junction rule, applies to the charge to a junction. Current is the flow of charge; thus, whatever charge flows into the junction must flow out. Kirchhoff’s second rule, also known as the loop rule, states that the voltage drop around a loop is zero.
• 10.5: Electrical Measuring Instruments
Voltmeters measure voltage, and ammeters measure current. Analog meters are based on the combination of a resistor and a galvanometer, a device that gives an analog reading of current or voltage. Digital meters are based on analog-to-digital converters and provide a discrete or digital measurement of the current or voltage. A voltmeter is placed in parallel with the voltage source to receive full voltage and must have a large resistance to limit its effect on the circuit. An ammeter is placed in
• 10.6: RC Circuits
An RC circuit is one that has both a resistor and a capacitor. The time constant τ for an RC circuit is τ=RC . When an initially uncharged capacitor in series with a resistor is charged by a dc voltage source, the capacitor asymptotically approaches the maximum charge. As the charge on the capacitor increases, the current exponentially decreases from the initial current.
• 10.7: Household Wiring and Electrical Safety
Electricity presents two known hazards: thermal and shock. A thermal hazard is one in which an excessive electric current causes undesired thermal effects, such as starting a fire in the wall of a house. A shock hazard occurs when an electric current passes through a person. Shocks range in severity from painful, but otherwise harmless, to heart-stopping lethality. In this section, we consider these hazards and the various factors affecting them in a quantitative manner.