Current, Voltage and Resistance

Electric circuits allow the flow of electrical energy to power devices. Three fundamental quantities describe how electricity behaves in a circuit:

I

Current

The rate of flow of electric charge.
Unit: Ampere (A)

Measured with an ammeter (connected in series)

V

Voltage

The energy per unit charge (electrical “push”).
Unit: Volt (V)

Measured with a voltmeter (connected in parallel)

R

Resistance

Opposition to the flow of current.
Unit: Ohm (Ω)

Depends on material, length, and thickness of conductor

Analogy: Think of electricity like water in a pipe. Voltage is the water pressure, current is the flow rate of water, and resistance is how narrow the pipe is. Higher pressure (voltage) pushes more water (current); a narrow pipe (resistance) reduces flow.

Ohm's Law

Ohm's Law describes the relationship between voltage, current, and resistance. It states that the voltage across a conductor is directly proportional to the current flowing through it, provided the temperature remains constant.

V = I × R

To find Voltage:

V = I × R

To find Current:

I = V / R

To find Resistance:

R = V / I

The VIR Triangle

Cover the quantity you want to find. What remains shows the formula: V on top means V = I × R.

Series and Parallel Circuits

Series Circuit

Components connected one after another in a single loop
Current is the same through all components
Voltage is shared across components
Total resistance: R_T = R₁ + R₂ + ...
If one component fails, the whole circuit breaks

Parallel Circuit

Components connected on separate branches
Voltage is the same across each branch
Current is split between branches
Total resistance: 1/R_T = 1/R₁ + 1/R₂ + ...
If one branch fails, others still work

Common Circuit Symbols

Battery

Resistor

Lamp

Switch (open)

Ammeter

Voltmeter

Wire

Variable Resistor

Key Vocabulary

Term	Definition
Current (I)	The rate of flow of electric charge, measured in amperes (A).
Voltage (V)	The potential difference (energy per unit charge) that drives current, measured in volts (V).
Resistance (R)	The opposition to current flow in a circuit, measured in ohms (Ω).
Ohm's Law	V = IR; voltage equals current multiplied by resistance.
Conductor	A material that allows electric current to flow easily (e.g., copper).
Insulator	A material that resists the flow of electric current (e.g., rubber, plastic).

Worked Examples

1

Find the current through a 10 Ω resistor with 20 V across it.

Given: V = 20 V, R = 10 Ω

Formula: I = V / R (rearranged from Ohm's Law)

Calculation: I = 20 / 10 = 2 A

Answer: The current through the resistor is 2 amperes.

2

Calculate the total resistance in a series circuit with three resistors: 4 Ω, 6 Ω, and 10 Ω.

Given: R₁ = 4 Ω, R₂ = 6 Ω, R₃ = 10 Ω

Formula (series): R_T = R₁ + R₂ + R₃

Calculation: R_T = 4 + 6 + 10 = 20 Ω

Answer: The total resistance is 20 ohms. If connected to a 12 V battery, the current would be I = 12/20 = 0.6 A.

3

Find the total resistance of two resistors (6 Ω and 12 Ω) in parallel.

Given: R₁ = 6 Ω, R₂ = 12 Ω

Formula (parallel): 1/R_T = 1/R₁ + 1/R₂

Step 1: 1/R_T = 1/6 + 1/12 = 2/12 + 1/12 = 3/12 = 1/4

Step 2: R_T = 4 Ω

Answer: The total resistance is 4 ohms. Note: In parallel, total resistance is always less than the smallest individual resistor.

Knowledge Check

Select the correct answer for each question. Click “Check Answer” to see feedback.

Question 1

A 6 V battery is connected to a 3 Ω resistor. What is the current?

18 A 0.5 A 2 A 9 A

Question 2

In a series circuit, two resistors of 5 Ω and 15 Ω are connected. What is the total resistance?

3.75 Ω 75 Ω 10 Ω 20 Ω

Question 3

A current of 3 A flows through a resistance of 8 Ω. What is the voltage across the resistor?

24 V 11 V 2.67 V 0.375 V

Question 4

In a parallel circuit, what is true about the voltage across each branch?

It is different for each branch It is the same across all branches It is always zero It doubles with each branch

Question 5

Two 10 Ω resistors are connected in parallel. What is their combined resistance?

20 Ω 10 Ω 5 Ω 100 Ω

Electricity and Circuits