Unit 9 ยท Lesson 2

๐Ÿ”ŒOhm's Law

V = IR

Ohm's Law: the voltage across a resistor is proportional to the current through it.

V = IR

A resistor that obeys Ohm's law is called ohmic. A plot of V vs. I is a straight line with slope R.

Non-ohmic devices (like diodes, lightbulbs at very high temperatures) don't follow a straight line โ€” their resistance changes.

Key insight: Ohm's law tells us that for a given resistor: - Larger voltage โ†’ larger current - Larger resistance โ†’ smaller current (for the same voltage)

โœ๏ธ Worked Example

Problem: A 12 V battery is connected to a 4 ฮฉ resistor. Find the current and power dissipated.

๐Ÿ“ Key Equations

Ohm's Law

V = IR
I = (V)/(R)
R = (V)/(I)

โš ๏ธ Common Mistakes

โŒ

Misconception: Ohm's Law applies to all circuit elements.

โœ“ Correct thinking: Ohm's Law only applies to ohmic (linear) resistors. Devices like diodes and LEDs are non-ohmic โ€” their resistance changes with voltage.

Why: Ohmic means the V vs. I graph is a straight line. Non-ohmic devices have curved V-I graphs, meaning R is not constant.

โŒ

Misconception: A higher resistance always means more power is dissipated.

โœ“ Correct thinking: It depends on what is held constant. At constant current, P = IยฒR so higher R means more power. At constant voltage, P = Vยฒ/R so higher R means LESS power.

Why: Always identify whether current or voltage is fixed before comparing power in different resistors.

โŒ

Misconception: Current is "used up" as it passes through a resistor.

โœ“ Correct thinking: Current is the same entering and leaving a resistor. What is "used up" is energy (voltage drops across the resistor).

Why: Charge is conserved โ€” no charge is created or destroyed in a resistor. The charges just lose energy (which becomes heat).

๐Ÿ“ Practice Problems

Try these problems. Check your answer when ready.

#1

A 6 V battery is connected to a resistor and 1.5 A of current flows. What is the resistance?

easy
#2

A resistor has R = 10 ฮฉ and 0.5 A flows through it. What is the voltage across it and power dissipated?

easy
#3

A V-I graph for a resistor shows a straight line passing through (0,0) and (6V, 2A). What is the resistance?

medium
#4

A student claims that doubling the voltage across a resistor doubles the power. Is this correct? Justify your answer.

medium
#5

A non-ohmic device shows the following V-I data: (2V, 1A), (4V, 1.5A), (6V, 1.8A). Is it ohmic? What can you say about how its resistance changes?

hard

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