Chapter 4: Series Circuits and Troubleshooting

Comprehensive practice flashcards covering Chapter 4: Resistors in Series, Ohm's Law Applications, Voltage Sources, Kirchhoff's Voltage Law, Voltage Dividers, Power, Ground References, and Troubleshooting.

What is the defining characteristic of resistors connected in series?

They form a single string that provides only one path for current between two points, meaning the current through each series resistor is the same.

Why does total resistance increase when additional resistors are placed in series?

Each resistor provides opposition to current in direct proportion to its resistance; adding more resistors creates more opposition to current, increasing total resistance.

What is the formula for the total resistance of $n$ equal-value resistors ($R$) connected in series?

$$R_T = n R$$

What is the total resistance of eight $22\,\Omega$ resistors connected in series?

$$R_T = 8 \times 22\,\Omega = 176\,\Omega$$

How does the current at any given point in a series circuit compare to the current at any other point?

The current is the same at all points in a series circuit because there is only one path for current flow.

If a series circuit contains a $100\,\Omega$ resistor and a $47\,\Omega$ resistor, and there are $20\,\text{mA}$ through the $100\,\Omega$ resistor, how much current flows through the $47\,\Omega$ resistor?

$$20\,\text{mA}$$

What is the typical forward voltage drop across a red LED operating within its normal range?

Approximately $1.7\,\text{V}$

What size current-limiting resistor is needed to limit the current to a red LED to $10\,\text{mA}$ from a $3.0\,\text{V}$ source, assuming the LED drops $1.7\,\text{V}$?

The voltage across the resistor is $3.0\,\text{V} - 1.7\,\text{V} = 1.3\,\text{V}$. Using Ohm's law: $R = \frac{1.3\,\text{V}}{10\,\text{mA}} = 130\,\Omega$.

What is the difference between series-aiding and series-opposing connections of voltage sources?

Series-aiding connections have the positive terminal of one source connected to the negative terminal of the next so their voltages add. Series-opposing connections have like terminals connected together, causing their voltages to subtract algebraically.

If one cell in a four-cell flashlight ($1.5\,\text{V}$ each) is accidentally installed backward, what is the resulting voltage across the bulb?

$3.0\,\text{V}$, because the reversed cell cancels out the voltage of one aiding cell ($1.5\,\text{V} + 1.5\,\text{V} + 1.5\,\text{V} - 1.5\,\text{V} = 3.0\,\text{V}$).

Who was Gustav Robert Kirchhoff, and when did he formulate his circuit laws?

A German physicist ($1824$-$1887$) who formulated his circuit laws in $1845$ as a student seminar exercise, which later became his doctoral dissertation.

What are the two common ways to state Kirchhoff's voltage law (KVL)?

1. The algebraic sum of all voltages around any closed path is zero ($\sum_{i=1}^n V_i = 0$). 2. The sum of all voltage drops around a closed path equals the total source voltage ($V_S = V_1 + V_2 + \dots + V_n$).

In a series circuit powered by a $25\,\text{V}$ source with three resistors, one voltage drop is $5\,\text{V}$ and another is $10\,\text{V}$. What is the third voltage drop?

$$V_3 = 25\,\text{V} - 5\,\text{V} - 10\,\text{V} = 10\,\text{V}$$

What is the general voltage-divider formula for finding the voltage drop $V_x$ across a series resistor $R_x$?

$$V_x = \left(\frac{R_x}{R_T}\right) V_S$$

In the radio receiver circuit shown, between which two stages is the potentiometer variable voltage divider connected?

Between the detector and the audio amplifier.

How does the potentiometer level sensor shown in this diagram convert liquid volume into an electrical signal?

A float inside the storage tank mechanically moves the wiper arm along the potentiometer resistive element, producing an output voltage directly proportional to the float position.

What circuit application of a series resistive voltage divider is depicted in this schematic?

A bias circuit for a transistor amplifier.

What three types of resistive sensors are commonly paired with a voltage divider to convert physical changes into an output voltage?

Thermistors, cadmium sulfide (CdS) cells, and strain gauges.

How is total power determined in a series resistive circuit?

By summing the individual power dissipations of each resistor: $P_T = P_1 + P_2 + P_3 + \dots + P_n$.

The resistors in a series circuit dissipate $1\,\text{W}$, $2\,\text{W}$, $5\,\text{W}$, and $8\,\text{W}$. What is the total power in the circuit?

$$P_T = 1\,\text{W} + 2\,\text{W} + 5\,\text{W} + 8\,\text{W} = 16\,\text{W}$$

In modern automotive electrical systems, which battery terminal connects directly to the chassis to establish reference ground?

The negative post.

What exception does Section 517 of the National Electrical Code (NEC) specify regarding reference grounding?

It specifies exceptions to standard grounding methods for hospital operating rooms and health care facilities.

Why can a digital multimeter (DMM) measure voltage between any two points in a circuit regardless of lead polarity, unlike an analog meter?

A DMM features a 'floating' common that indicates positive or negative values automatically, whereas an analog meter's common lead must be connected to the most negative point to keep the needle from deflecting backward.

If the voltage between terminals A and B ($V_{AB}$) is measured as $5.0\,\text{V}$, what is the value of $V_{BA}$?

$$-5.0\,\text{V}$$

What are the ideal resistance values of an open circuit and a short circuit?

An open circuit has infinite resistance ($\infty\,\Omega$), while a short circuit has zero resistance ($0\,\Omega$).

What happens to the current and component voltages when a series circuit opens?

Current drops to $0\,\text{A}$, the voltage across all intact components becomes $0\,\text{V}$, and the full source voltage appears across the open component.

What three potential physical causes of unwanted short circuits are illustrated on this printed circuit board?

Shorted leads, a wire clipping, and a solder splash.

What effect does a short circuit across a component have on total circuit current and voltage across that component?

Total series resistance decreases, which causes total circuit current to increase; the voltage drop across the shorted component drops to essentially $0\,\text{V}$.

How can a technician isolate a shorted resistor in a powered series circuit?

By measuring the voltage across each resistor in the series string; the shorted component will measure $0\,\text{V}$.