Grade 10

Advanced

6 min

Lesson 3 of 12

Current, Resistance, and Ohm's Law

Not Started

Focuses on the flow of charge and the factors that oppose that flow in a circuit.

Why does your smartphone get warm during a heavy game, and why would using a 10-foot charging cable slow down your charge? The answer lies in the invisible 'friction' of the subatomic world.

Learning Objectives

1.Calculate current, voltage, and resistance using Ohm's Law in complex circuit scenarios.
2.Predict how changes in a conductor's length, area, material, and temperature alter its resistance.
3.Differentiate between Ohmic and Non-Ohmic conductors by analyzing Current-Voltage (I-V) characteristic graphs.

Ohm's Law: The Fundamental Balance

In any electrical circuit, there is a constant tug-of-war between the Potential Difference (

V

), which pushes charge, and Resistance (

R

), which opposes it. This relationship is defined by Ohm's Law, stating that the current (

I

) flowing through a conductor is directly proportional to the voltage across it, provided temperature remains constant. Mathematically, we express this as

V = I \times R

. Here,

V

is measured in Volts (V),

I

in Amperes (A), and

R

in Ohms (

\Omega

). Think of it like water in a pipe: Voltage is the pump pressure, Current is the flow rate, and Resistance is the narrowness of the pipe. If you increase the pressure (

V

), the flow (

I

) increases; if you clog the pipe (

R

), the flow decreases.

A heating element is connected to a $240\text{ V}$ supply. If the resistance of the element is $48\text{ }\Omega$ , what is the current flowing through it?

1. Identify knowns: $V = 240\text{ V}$ , $R = 48\text{ }\Omega$ . 2. Rearrange Ohm's Law for current: $I = \frac{V}{R}$ . 3. Substitute values: $I = \frac{240}{48}$ . 4. Calculate: $I = 5\text{ A}$ .

Quick Check

If the resistance in a circuit is tripled while the voltage remains constant, what happens to the current?

Look at the inverse relationship between

I

and

R

I = \frac{V}{R}

Answer

The current will be reduced to one-third of its original value.

The Four Factors of Resistance

Resistance isn't random; it is determined by the physical properties of the conductor. We use the formula

R = \rho \frac{L}{A}

to understand this. First, Length (

L

): a longer wire means more atoms for electrons to bump into, increasing resistance. Second, Cross-sectional Area (

A

): a thicker wire provides more 'lanes' for electrons, decreasing resistance. Third, Material (Resistivity,

\rho

): some materials like Copper hold onto electrons loosely, while others like Nichrome hold them tightly. Finally, Temperature: as a conductor heats up, its atoms vibrate more violently, making it harder for electrons to pass through, thus increasing resistance.

Wire A has a length $L$ and area $A$ . Wire B is made of the same material but is $3$ times longer ( $3L$ ) and has half the area ( $0.5A$ ). How many times greater is the resistance of Wire B?

1. Formula for Wire A: $R_A = \rho \frac{L}{A}$ . 2. Formula for Wire B: $R_B = \rho \frac{3L}{0.5A}$ . 3. Simplify Wire B: $R_B = \rho \frac{L}{A} \times \frac{3}{0.5} = R_A \times 6$ . 4. Result: Wire B has $6$ times the resistance of Wire A.

Quick Check

Why does a lightbulb's resistance increase shortly after you flip the switch?

Think about the fourth factor of resistance.

Answer

As the filament glows, its temperature increases, causing the atoms to vibrate more and increase the resistance.

I-V Characteristics: Ohmic vs. Non-Ohmic

We can visualize how a component behaves by plotting an I-V Graph (Current vs. Voltage). For an Ohmic Conductor (like a standard resistor at constant temperature), the graph is a straight line passing through the origin. The constant slope indicates that resistance is constant ( $R = \frac{V}{I}$ ). However, Non-Ohmic components do not follow this linear rule. A Filament Lamp curve flattens out as voltage increases because the heat increases resistance. A Diode only allows current in one direction, showing zero current for negative voltage and a sharp spike once a threshold positive voltage is reached.

On an I-V graph where Current ( $I$ ) is on the y-axis and Voltage ( $V$ ) is on the x-axis, you have two lines. Line 1 is steep, and Line 2 is shallow. Which represents the higher resistance?

1. Recall $R = \frac{V}{I}$ . 2. On this graph, the slope is $\frac{\Delta I}{\Delta V} = \frac{1}{R}$ . 3. A steeper slope means a larger $\frac{1}{R}$ , which implies a smaller $R$ . 4. Therefore, the shallower line (Line 2) represents the higher resistance.

Key Takeaways

1Ohm's Law ( $V=IR$ ) defines the linear relationship between voltage, current, and resistance in Ohmic conductors.
2Resistance is directly proportional to length and resistivity, but inversely proportional to cross-sectional area ( $R = \rho \frac{L}{A}$ ).
3Temperature increases resistance in metallic conductors due to increased atomic vibrations.
4Ohmic conductors produce a straight-line I-V graph, while non-Ohmic conductors like bulbs and diodes produce curved lines.

Quick Check

Multiple Choice

A wire is replaced with another wire of the same material and length, but with twice the diameter. What is the new resistance?

Multiple Choice

Which of the following would produce a non-linear I-V characteristic graph?

True/False

In an I-V graph where Current is on the y-axis, a steeper slope indicates a higher resistance.

What's Next?

Review Tomorrow

In 24 hours, try to sketch the I-V graphs for a resistor, a filament lamp, and a diode from memory, and write down the formula for resistance based on physical dimensions.

Practice Activity

Find a household appliance label (like a toaster or charger), note the Voltage and Current, and calculate its internal resistance using $R = V/I$ .

Browse

Browse

Current, Resistance, and Ohm's Law

Learning Objectives

Ohm's Law: The Fundamental Balance

The Four Factors of Resistance

I-V Characteristics: Ohmic vs. Non-Ohmic

Key Takeaways

Quick Check

What's Next?

Current, Resistance, and Ohm's Law

Learning Objectives

Ohm's Law: The Fundamental Balance

The Four Factors of Resistance

I-V Characteristics: Ohmic vs. Non-Ohmic

Key Takeaways

Quick Check

What's Next?