recall and use V = IR

Resistance and Resistivity ⚡️

What is Resistance?

Resistance is the property of a material that opposes the flow of electric current. Think of it like a crowded hallway – the more people (electrons) there are, the harder it is to move through. The unit of resistance is the ohm (Ω).

Ohm’s Law

Ohm’s Law links voltage (V), current (I) and resistance (R) in a simple equation:

$$V = IR$$

- V is the voltage across the component (volts, V). - I is the current flowing through it (amperes, A). - R is the resistance (ohms, Ω).

Calculating Resistance

If you know any two of the variables, you can find the third:

• R = V / I
• I = V / R
• V = I × R

Resistivity: Material Property

Resistivity (ρ) describes how strongly a material resists current. It depends on the material, not on its shape. The resistance of a uniform wire is:

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

- L = length of the wire (m). - A = cross‑sectional area (m²). - ρ = resistivity (Ω·m).

Examples & Practice

1. Find the resistance of a 2 m long copper wire with a cross‑sectional area of 1.0 mm².
   • Convert area: 1.0 mm² = 1.0×10⁻⁶ m².
   • Use R = ρL/A: R = (1.68×10⁻⁸ Ω·m)(2 m)/(1.0×10⁻⁶ m²) = 0.0336 Ω.
2. Determine the current flowing through a 12 V battery connected to a 4 Ω resistor.
   • Use I = V/R: I = 12 V / 4 Ω = 3 A.
3. Calculate the voltage drop across a 5 Ω resistor when 2 A of current flows through it.
   • Use V = IR: V = 2 A × 5 Ω = 10 V.

Summary 📐

• Resistance (R) is measured in ohms (Ω) and opposes current flow.
• Ohm’s Law: $V = IR$ links voltage, current and resistance.
• Resistivity (ρ) is a material constant; resistance depends on length and area: $R = \rho L/A$.
• Use the formulas to solve for any unknown in a circuit problem.
• Remember: lower resistivity → easier flow of electrons (e.g., copper vs. glass).