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Year 11 Science

Circuits and Resistors

Analyse series and parallel circuits, calculate total resistance using Ohm's law, and explore Kirchhoff's laws for understanding voltage and current distribution.

Ohm's Law and Circuit Fundamentals

Ohm's law describes the relationship between voltage (V), current (I) and resistance (R) in a circuit: V = IR. Voltage is the energy per unit charge (volts, V), current is the rate of charge flow (amperes, A), and resistance opposes current flow (ohms, Ω).

V

Voltage (V)

The "push" that drives charge around the circuit. Measured in volts (V). Supplied by a battery or power supply.

I

Current (I)

The rate of flow of electric charge. Measured in amperes (A). Conventional current flows from positive to negative.

R

Resistance (R)

Opposition to current flow. Measured in ohms (Ω). Higher resistance means less current for a given voltage.

Ohm's Law rearrangements: V = IR  |  I = V/R  |  R = V/I. These three forms let you find any unknown quantity if you know the other two.

Series and Parallel Circuits

Components can be connected in series (one path for current) or in parallel (multiple paths for current). Each arrangement has different rules for current, voltage and resistance.

Series Circuit

+
R1
R2
-

Current: Same through all components (IT = I1 = I2)

Voltage: Shared across components (VT = V1 + V2)

Resistance: RT = R1 + R2 + ...

Parallel Circuit

+
R1
R2
-

Current: Splits between branches (IT = I1 + I2)

Voltage: Same across each branch (VT = V1 = V2)

Resistance: 1/RT = 1/R1 + 1/R2 + ...

Key insight: Adding resistors in series increases total resistance. Adding resistors in parallel decreases total resistance (because current has more paths to flow through).

Introduction to Kirchhoff's Laws

Kirchhoff's laws provide powerful tools for analysing complex circuits with multiple loops and junctions.

Junction Rule (KCL)

Kirchhoff's Current Law: The total current entering a junction equals the total current leaving it.

ΣIin = ΣIout

Based on conservation of charge -- charge cannot be created or destroyed at a junction.

Loop Rule (KVL)

Kirchhoff's Voltage Law: The sum of all voltage gains and drops around any closed loop equals zero.

ΣV = 0 around a loop

Based on conservation of energy -- energy gained from the battery equals energy lost across resistors.

Practical Application

In household wiring, appliances are connected in parallel. This ensures each appliance receives the full mains voltage (230 V in Australia) and can be switched on/off independently. If one appliance fails, the others continue to work because current has alternative paths.

Key Vocabulary

Ohm's Law

The relationship V = IR, stating that voltage across a conductor is proportional to current through it (at constant temperature).

Resistance (Ω)

The opposition to current flow in a circuit, measured in ohms. Determined by material, length, cross-sectional area and temperature.

Series Circuit

A circuit with only one path for current. Components share the same current but divide the voltage.

Parallel Circuit

A circuit with multiple paths for current. Components share the same voltage but divide the current.

Worked Examples

1

Two resistors (6 Ω and 12 Ω) are connected in series to a 9 V battery. Find the total resistance and current.

Step 1: RT = R1 + R2 = 6 + 12 = 18 Ω.

Step 2: I = V / RT = 9 / 18 = 0.50 A.

Answer: Total resistance is 18 Ω and current through the circuit is 0.50 A (same through both resistors in series).

2

Two resistors (6 Ω and 12 Ω) are connected in parallel. Find the total resistance.

Step 1: 1/RT = 1/R1 + 1/R2 = 1/6 + 1/12 = 2/12 + 1/12 = 3/12.

Step 2: 1/RT = 3/12 = 1/4.

Answer: RT = 4 Ω. Note this is less than the smallest individual resistor -- a key feature of parallel circuits.

3

Use Kirchhoff's voltage law: A 12 V battery is connected to three resistors in series. V1 = 3 V and V2 = 5 V. Find V3.

Step 1: KVL states: Vbattery = V1 + V2 + V3.

Step 2: 12 = 3 + 5 + V3.

Answer: V3 = 12 - 3 - 5 = 4 V.

Knowledge Check

Select the correct answer for each question. Click "Check Answer" to see if you are right.

Question 1

A 12 V battery drives a current of 3 A through a resistor. What is the resistance?

Question 2

In a series circuit, the current through each component is:

Question 3

Three 12 Ω resistors are connected in parallel. The total resistance is:

Question 4

Kirchhoff's current law (junction rule) is based on the conservation of:

Question 5

In a parallel circuit, adding more resistors:

Key Concepts Summary

Year 11: Light and EM Waves