Ohm's Law

Lesson 1 of 4: Electrical Circuits

In this lesson:

• Define current and calculate using
• Apply Ohm's Law:
• Explain resistance and read V-I graphs

Learning Objectives for This Lesson

1. Define current:
2. Apply for voltage, current, resistance
3. Explain resistance and its factors
4. Distinguish ohmic from non-ohmic materials
5. Interpret V-I graphs for both device types

Voltage, Current, Resistance — A Preview

Voltage = pressure · Current = flow rate · Resistance = pipe narrowness

Electric Current Definition and Formula

• Current = rate of charge flow through a conductor
• where is charge (C), is time (s)
• SI unit: ampere (A) = coulomb per second (C/s)
• Current requires a closed circuit — any gap stops flow entirely

Conventional Current vs. Electron Flow

• Electrons (negative) flow from − to + terminal
• Conventional current (positive) is defined as + to − direction
• For all circuit calculations: use conventional current — results are correct

Worked Example: Current from Charge and Time

Given: ,

Find: Current

Solution:

A current of 3 amperes flows through the conductor.

Quick Check: Calculate the Current

A wire carries 12 C of charge past a point in 4 s.

What is the current in the wire?

Think first — then advance for the answer.

Ohm's Law:

• For ohmic materials: current is proportional to voltage
• where = voltage (V), = current (A), = resistance (Ω)
• The ohm:
• Ohm's Law applies to certain materials, not universally

Three Forms of Ohm's Law

Write the formula first, then substitute.

Worked Example: Find the Voltage

Given: ,

Find: Voltage

A potential difference of 8 volts appears across the resistor.

Worked Example: Find the Current

Given: (battery), (resistor)

Find: Current

A current of 60 milliamperes flows through the circuit.

Worked Example: Find the Resistance

Given: ,

Find: Resistance

The component has a resistance of 24 ohms.

Quick Check: Apply Ohm's Law

A 100 Ω resistor has 5 V across it.

What current flows through it?

Write the formula, substitute, check units.

Resistance — The Collision Model

• Electrons moving through a metal collide with vibrating lattice atoms
• Each collision transfers energy as heat and slows electron flow
• That opposition to flow is resistance

Four Factors That Affect Resistance

Resistance Formula and Real Applications

• = resistivity (Ω·m) — a material property
  • Copper: Ω·m
  • Rubber: Ω·m
• Long, thin wire = high resistance (why extension cords can cause problems)

Quick Check: Resistance and Wire Length

A copper wire has resistance .

Qualitatively — what happens to if:

• The length doubles?
• The diameter doubles (area increases by 4)?

Use — no numbers needed.

Ohmic vs. Non-Ohmic: V-I Graphs

• Ohmic: straight line through origin — slope = (constant)
• Non-ohmic: curved line — resistance changes with voltage or current

Non-Ohmic Devices and Their Behavior

• Light bulb (tungsten): resistance increases as filament heats — curve bows upward
• Diode: conducts in one direction (forward bias), almost nothing in reverse
• Thermistor: resistance decreases with temperature — used as temp sensor

Non-ohmic devices are designed for specific behaviors.

Worked Example: Reading a V-I Graph

Ohmic resistor: when

Light bulb: at is 5 Ω; at is 30 Ω

→ Resistance grew with voltage and temperature

Worked Example: Identifying Ohmic Devices

Which curve shows an ohmic device?

• Curve A: straight line, slope = constant
• Curve B: curves upward — slope increases with V
• Curve C: steep, then flat — diode behavior

→ Curve A is ohmic. The slope (= ) is the same everywhere.

Quick Check: Reading V-I Graphs

A V-I graph curves upward as V increases.

• Is this device ohmic or non-ohmic?
• Is its resistance increasing or decreasing?
• What real device does this describe?

Practice: Three Ohm's Law Problems

Write the formula first:

1. 30 C flows through a wire in 10 s. Find .
2. , . Find .
3. , . Find .

Try all three before the next slide.

Answers: Check Your Practice Work

3. — this gives R at one operating point only

Key Takeaways: Current, Voltage, Resistance

✓ — current is charge flow rate (unit: A)

✓ — Ohm's Law links voltage, current, resistance

✓ — resistance depends on material, length, and area

Watch Out: Avoid These Three Errors

Voltage doesn't flow — current flows. Voltage is a difference between two points.

Higher → less current (not more): — R is in the denominator.

Conventional current direction matters — especially for magnetic effects in sec-20-1.

What Comes Next: Series Circuits

sec-19-2: Series Circuits

• Resistors end-to-end in a single loop
• One path for current — same everywhere
• Equivalent resistance:
• Kirchhoff's Voltage Law — energy bookkeeping

skills apply to every component in the circuit.