Strand 9 Technical Math & Science for DC Electronic Circuits

Electric charge

A property of matter that causes electrical effects.

Current

The rate of flow of charge past a point, defined as $I = \frac{Q}{t}$.

Voltage

The electrical potential difference, defined as $V = \frac{W}{Q}$.

Resistance

A measure of how much a component opposes current for a given voltage, measured in ohms $\Omega$.

Conductance

The ease of conducting current, measured in siemens $S$ and defined as $G = \frac{1}{R}$.

Power

The rate of energy transfer, defined as $P = V I$.

Passive sign convention

The convention where current entering the positive terminal of a component is defined as absorbing power.

SI unit for current

Ampere $\text{A}$.

SI unit for voltage

Volt $\text{V}$.

SI unit for resistance

Ohm $\Omega$.

SI unit for power

Watt $\text{W}$.

SI unit for charge

Coulomb $\text{C}$.

Capacitance unit

Farad $\text{F}$.

Charge-current relationship

Charge is related to current by the formula $I = \frac{Q}{t}$.

Voltage-energy relationship

Voltage is given by $V = \frac{W}{Q}$.

Current entering a node

According to Kirchhoff's Current Law (KCL), the total current entering equals the total current leaving at a node.

Voltage sum in a loop

According to Kirchhoff's Voltage Law (KVL), the sum of voltages around a closed loop equals zero.

Equivalent resistance in series

$R_{\text{eq}} = R_1 + R_2 + \cdots + R_n$.

Equivalent resistance in parallel

$\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots + \frac{1}{R_n}$.

Ohm's Law formula

$V = I R$.

Time constant of RC circuit

$\tau = R C$, which represents the time it takes for a capacitor to charge or discharge.

Current through R_L in a voltage divider

$I_{R_L} = I_{in} \frac{R_2}{R_1 + R_2}$ in a two-branch parallel network.

Power dissipated in a resistor

$P = I^2 R$ or $P = \frac{V^2}{R}$.

Energy stored in a capacitor

$E = \frac{1}{2} C V^2$.

Zener diode function

Provides a constant output voltage by breaking down at a specified reverse voltage.

Ammeter connection

Placed in series in the circuit to measure current.

Voltmeter connection

Connected in parallel across a component to measure voltage.

Ohmmeter rule

Power must be off when measuring resistance.

Capacitor behavior in steady state

In DC steady state, a capacitor behaves like an open circuit.

Inductor behavior in steady state

In DC steady state, an inductor behaves like a short circuit.

Timed voltage across a charging capacitor

$V_C(t) = V_s \left(1 - e^{-t/\tau}\right)$.

LED current limiting resistor

Calculated using $R = \frac{V_s - V_F}{I}$ to protect the LED.

Voltage drop across a forward-biased diode

Typically around $0.7V$ for silicon diodes.

Current divider formula

$I_1 = I_{in} \frac{R_2}{R_1 + R_2}$ for two resistors in parallel.

Thevenin equivalent resistance

$R_{\text{th}}$: the resistance seen at the terminals when independent sources are turned off.

Maximum power transfer condition

Occurs when the load resistance equals the Thevenin resistance $R_L = R_{\text{th}}$.

Troubleshooting open circuit

Symptoms include floating voltages and no current flow.

Troubleshooting short circuit

Symptoms include excessive current, voltage sag, and blown fuses.

Significant figures in calculations

It's important to track significant figures to avoid accumulating errors.

Sign convention in KVL

Define rises and drops consistently while traversing a loop.

Measurement error due to meter loading

Affects readings when the meter's input resistance is not infinitely high.

Voltage divider output voltage formula

$V_{out} = V_{in} \frac{R_2}{R_1 + R_2}$ for series resistors.

Capacitance unit prefixes

Common prefixes include $\mu F$ (microfarads) and $n F$ (nanofarads).