๐Ohm'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)
โ๏ธ Worked Example
Problem: A 12 V battery is connected to a 4 ฮฉ resistor. Find the current and power dissipated.
๐ Key Equations
Ohm's Law
V = IRI = (V)/(R)R = (V)/(I)โ ๏ธ Common Mistakes
Misconception: Ohm's Law applies to all circuit elements.
โ 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.
Misconception: A higher resistance always means more power is dissipated.
โ 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.
Misconception: Current is "used up" as it passes through a resistor.
โ 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).
๐ Practice Problems
Try these problems. Check your answer when ready.
A 6 V battery is connected to a resistor and 1.5 A of current flows. What is the resistance?
A resistor has R = 10 ฮฉ and 0.5 A flows through it. What is the voltage across it and power dissipated?
A V-I graph for a resistor shows a straight line passing through (0,0) and (6V, 2A). What is the resistance?
A student claims that doubling the voltage across a resistor doubles the power. Is this correct? Justify your answer.
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?
Finished reading through this lesson?