Series and Parallel Circuits

Series and Parallel Circuits

High School

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Learning Objectives

Key Vocabulary

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Series Circuit

A circuit where components are connected end-to-end, providing a single path for the current.

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Parallel Circuit

A circuit that provides multiple pathways for the electric current to flow through different branches.

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Voltage (V)

The electrical potential difference or ‘push’ that moves electric charges through a circuit, measured in volts.

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Current (I)

The rate of flow of electric charge through a conductor, measured in amperes (A) or amps.

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Resistance (R)

The measure of the opposition to current flow in an electrical circuit, measured in ohms (Ω).

Building Blocks: Voltage, Current, Resistance

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Voltage (V)

• ​Voltage is the 'push' that moves electrons around a circuit.

• ​​It is usually supplied by a power source like a battery.

• ​This is like a pump creating pressure to move water through pipes.

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Current (I)

• ​Current is the flow of electric charge, or electrons, through a circuit.

• ​​A faster flow of these electrons means that there is higher current.

• ​This is like the amount of water flowing through a given pipe.

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Resistance (R)

• ​Resistance slows down the overall flow of electrons in the electrical circuit.

• ​​It is like sand inside a pipe that impedes the water flow.

• ​As a circuit's resistance increases, the electric current will always decrease.

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Solved Example 1
A simple circuit has a resistance of 3 ohms and a current of 4 amps flowing through it. What is the voltage of the battery?

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Step 1: Analyze and Sketch the Problem

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Solved Example 1
A simple circuit has a resistance of 3 ohms and a current of 4 amps flowing through it. What is the voltage of the battery?

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Step 2: Solve for the Unknown

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Solved Example 1
A simple circuit has a resistance of 3 ohms and a current of 4 amps flowing through it. What is the voltage of the battery?

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Step 3: Evaluate the Answer

Multiple Choice

As the resistance of a circuit with a constant voltage source increases, what happens to the current?

• It increases.

• It decreases.

• It stays the same.

• It reverses direction.

Ohm's Law: The V-I-R Relationship

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Solved Example 2
A simple circuit has a 12-volt battery and a resistor with 3 ohms of resistance. How much current is flowing through the circuit?

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Step 1: Analyze and Sketch the Problem

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Solved Example 2
A simple circuit has a 12-volt battery and a resistor with 3 ohms of resistance. How much current is flowing through the circuit?

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Step 2: Solve for the Unknown

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Solved Example 2
A simple circuit has a 12-volt battery and a resistor with 3 ohms of resistance. How much current is flowing through the circuit?

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Step 3: Evaluate the Answer

Multiple Choice

What is the resistance of a lightbulb that experiences a voltage of 9 Volts and allows a current of 3 amps to flow?

• 3 ohms

• 27 ohms

• 12 ohms

• 1/3 ohms

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Series Circuits: The Single Path

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Solved Example 3
A series circuit contains a 9V battery and three resistors with values of 3 Ω, 10 Ω, and 5 Ω. What is the total current flowing through the circuit?

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Step 1: Analyze and Sketch the Problem

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Solved Example 3
A series circuit contains a 9V battery and three resistors with values of 3 Ω, 10 Ω, and 5 Ω. What is the total current flowing through the circuit?

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Step 2: Solve for the Unknown

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Solved Example 3
A series circuit contains a 9V battery and three resistors with values of 3 Ω, 10 Ω, and 5 Ω. What is the total current flowing through the circuit?

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Step 3: Evaluate the Answer

Multiple Choice

In a series circuit with three resistors, which quantity remains the same through each resistor?

• Voltage

• Current

• Resistance

• Power

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Parallel Circuits: Multiple Paths

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Solved Example 4
A parallel circuit contains three resistors with values of 10 Ω, 20 Ω, and 30 Ω. What is the total resistance of the circuit?

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Step 1: Analyze and Sketch the Problem

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Solved Example 4
A parallel circuit contains three resistors with values of 10 Ω, 20 Ω, and 30 Ω. What is the total resistance of the circuit?

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Step 2: Solve for the Unknown

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Solved Example 4
A parallel circuit contains three resistors with values of 10 Ω, 20 Ω, and 30 Ω. What is the total resistance of the circuit?

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Step 3: Evaluate the Answer

• In a parallel circuit, the total resistance is always less than the smallest individual resistance. The smallest resistor in this circuit is 10 Ω.

• Our calculated total resistance is approximately 5.45 Ω, which is less than 10 Ω, confirming the answer is reasonable and correct.

Multiple Choice

What is the primary advantage of a parallel circuit over a series circuit for household wiring?

• The current is the same through all appliances.

• The total resistance is higher.

• It uses less wire.

• If one appliance fails, the others can still operate.

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Common Misconceptions About Circuits

Misconception	Correction
In a parallel circuit, if one bulb fails, others dim.	The other bulbs' brightness stays the same as voltage is unchanged.
More resistors in a parallel circuit increase the total resistance.	More resistors in parallel create more paths, decreasing total resistance.
Current is used up as it passes through a resistor.	Current is conserved; electrical energy is converted into other forms.

Multiple Choice

If a fourth lightbulb is added to a series circuit that already has three bulbs, what is the effect on the total resistance and the overall brightness of the bulbs?

• Total resistance increases, and bulbs get dimmer.

• Total resistance increases, and bulbs get brighter.

• Total resistance decreases, and bulbs get dimmer.

• Total resistance decreases, and bulbs get brighter.

Multiple Choice

Why do the lightbulbs in a parallel circuit with two identical bulbs glow brighter than the bulbs in a series circuit with two identical bulbs, assuming the same voltage source?

• Because the series circuit divides the current between the two bulbs.

• Because each bulb in the parallel circuit receives the full source voltage, unlike in the series circuit where voltage is divided.

• Because the parallel circuit has a higher total resistance, leading to more power.

• Because the current is the same in both circuits.

Multiple Choice

Analyze a parallel circuit with a 12V battery and two branches containing resistors of 6 Ω and 12 Ω. How does the current in the 6 Ω branch compare to the 12 Ω branch, and what is the total current leaving the battery?

• The current is higher in the 6 Ω branch; total current is 3 A.

• The current is the same in both branches; total current is 2 A.

• The current is lower in the 6 Ω branch; total current is 1 A.

• The current is higher in the 12 Ω branch; total current is 3 A.

Multiple Choice

You have three resistors: 5 Ω, 10 Ω, and 20 Ω. To achieve the lowest possible total resistance for the circuit, how should you arrange them, and what would this resistance be?

• Arrange them in parallel for a total resistance of 35 Ω.

• Arrange them in parallel for a total resistance of approximately 2.86 Ω.

• Arrange them in series for a total resistance of 2.86 Ω.

• Arrange them in series for a total resistance of 35 Ω.

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Summary

Poll

On a scale of 1-4, how confident are you about the concepts covered in today's review?

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