Current, Voltage and Resistance

Definition: Voltage is the energy per unit charge that drives electric current through a circuit.

Formula: Let $V$ be the voltage, $W$ be the energy in joules, and $Q$ be the charge in coulombs:

$V = \frac{W}{Q}$

Units: Voltage is measured in volts (V).

$1\ \text{V} = \frac{1\ \text{J}}{1\ \text{C}}$

Example: If 12 joules of energy are used to move 4 coulombs of charge, find the voltage.

Step 1: Write the known values:

$W = 12\ \text{J},\quad Q = 4\ \text{C}$

Step 2: Use the formula:

$V = \frac{W}{Q}$

Step 3: Substitute the values:

$V = \frac{12}{4}$

Step 4: Simplify:

$V = 3\ \text{V}$

Final Answer: The voltage is $3\ \text{V}$.

Definition: Resistance is the opposition that a material offers to the flow of electric current.

Formula (Ohm's Law): Let $V$ be the voltage, $I$ be the current, and $R$ be the resistance:

$V = IR$

Rearranging for resistance:

$R = \frac{V}{I}$

Units: Resistance is measured in ohms (Ω).

Example: If a current of 2A flows through a resistor with 10V across it, find the resistance.

Step 1: Write the known values:

$V = 10\ \text{V},\quad I = 2\ \text{A}$

Step 2: Use the formula:

$R = \frac{V}{I}$

Step 3: Substitute the values:

$R = \frac{10}{2}$

Step 4: Simplify:

$R = 5\ \Omega$

Final Answer: The resistance is $5\ \Omega$.

Definition: Ohm's Law states that the current $I$ flowing through a conductor is directly proportional to the voltage $V$ across it and inversely proportional to the resistance $R$.

$V = IR$

If the resistance is constant, the current increases with an increase in voltage.

Resistance is measured in ohms (Ω).

Common Units:

Milli-ohm:

$1\ \text{m}\Omega = 10^{-3}\ \Omega$

Kilo-ohm:

$1\ \text{k}\Omega = 10^{3}\ \Omega$

Mega-ohm:

$1\ \text{M}\Omega = 10^{6}\ \Omega$

Example 1: Convert $5\ \text{k}\Omega$ to ohms

Step 1: Use conversion formula:

$1\ \text{k}\Omega = 10^3\ \Omega$

Step 2: Multiply:

$5\ \text{k}\Omega = 5 \times 10^3 = 5000\ \Omega$

Final Answer: $5\ \text{k}\Omega = 5000\ \Omega$

Example 2: Convert $0.02\ \Omega$ to milli-ohms

Step 1: Use conversion formula:

$1\ \text{m}\Omega = 10^{-3}\ \Omega \Rightarrow 1\ \Omega = 1000\ \text{m}\Omega$

Step 2: Multiply:

$0.02\ \Omega = 0.02 \times 1000 = 20\ \text{m}\Omega$

Final Answer: $0.02\ \Omega = 20\ \text{m}\Omega$

Example 3: Convert $2.5\ \text{M}\Omega$ to ohms

Step 1: Use conversion formula:

$1\ \text{M}\Omega = 10^6\ \Omega$

Step 2: Multiply:

$2.5\ \text{M}\Omega = 2.5 \times 10^6 = 2{,}500{,}000\ \Omega$

Final Answer: $2.5\ \text{M}\Omega = 2{,}500{,}000\ \Omega$

Name	Symbol	Conversion	Example
Milli-ohm	mΩ	$1\ \text{m}\Omega = 10^{-3}\ \Omega$	$R_0 = 10\ \text{m}\Omega$
Ohm	Ω	—	$R_1 = 10\ \Omega$
Kilo-ohm	kΩ	$1\ \text{k}\Omega = 10^3\ \Omega$	$R_2 = 2\ \text{k}\Omega$
Mega-ohm	MΩ	$1\ \text{M}\Omega = 10^6\ \Omega$	$R_3 = 5\ \text{M}\Omega$

A resistor is an electrical component that is specifically designed to resist the flow of electric current. It provides a known resistance to current in a circuit and is used to control the amount of current or divide voltage.

Types of Resistors:

1. Fixed Resistors: These resistors have a constant resistance value that does not change with current or voltage.
2. Variable Resistors: These resistors allow the resistance to be adjusted manually. Examples include:

Rheostat : used to control current

Potentiometer : used to control voltage

Function of a Resistor in a Circuit:

Resistors limit current, divide voltages, and protect components by ensuring that excessive current doesn't flow through the circuit.

Ohm's Law is used to calculate the current, voltage, or resistance in a circuit:

$V = IR$

Where: $V$ = Voltage (in volts) $I$ = Current (in amperes) $R$ = Resistance (in ohms)

Examples Using Resistors:

Example 1: A resistor has a resistance of $R = 100\ \Omega$, and a voltage of $V = 12\ \text{V}$ is applied across it. What is the current flowing through the resistor?

Step 1: Use Ohm's Law: $V = IR$

Step 2: Rearrange to find current: $I = \frac{V}{R}$

$I = \frac{12\ \text{V}}{100\ \Omega} = 0.12\ \text{A}$

Final Answer: $I = 0.12\ \text{A}$

Example 2: What resistance is needed to allow a current of $0.5\ \text{A}$ to flow when a voltage of $6\ \text{V}$ is applied?

Step 1: Use Ohm's Law: $V = IR$

Step 2: Rearrange to find resistance: $R = \frac{V}{I}$

$R = \frac{6\ \text{V}}{0.5\ \text{A}} = 12\ \Omega$

Final Answer: $R = 12\ \Omega$

Example 3: A resistor of $47\ \Omega$ has a current of $0.2\ \text{A}$ flowing through it. What is the voltage across the resistor?

Step 1: Use Ohm's Law: $V = IR$

$V = 0.2\ \text{A} \times 47\ \Omega = 9.4\ \text{V}$

Final Answer: $V = 9.4\ \text{V}$