AP Physics C: E&M Unit 11 Cheatsheet: Electric Circuits

Current is the rate of charge flow:

• I = dq/dt (scalar, but has direction)
• Direction: conventional current = positive charge motion
• Electrons actually move opposite to conventional current

Drift velocity relates microscopic motion to macroscopic current:

• I = nqv_dA
• n = charge carrier density
• v_d = average drift velocity (very slow!)
• A = cross-sectional area

Key distinction: If I = 0, charge carriers still move randomly; net motion is zero.

Current density J is current per unit area (vector):

• I = ∫ J · dA
• J = nqv_d

Relationship to electric field:

• E = ρJ
• ρ = resistivity (material property)
• Stronger field needed for same J in high-resistivity materials

Integration: If J(r) varies across cross-section, integrate to find total current.

Resistance opposes charge flow:

• R = ρℓ/A
• ρ = resistivity (material)
• ℓ = length, A = cross-sectional area

Resistivity facts:

• Increases with temperature (for conductors)
• Constant for ohmic materials
• For non-uniform resistivity: R = ∫ ρ(ℓ) dℓ/A

Ohm's Law: I = ΔV/R

• Applies to ohmic materials (constant R)
• Slope of I vs. ΔV graph = 1/R

Power dissipated or transferred:

• P = I·ΔV (fundamental)
• P = I²R (resistive dissipation)
• P = (ΔV)²/R (alternative form)

Interpretation:

• Brightness of lightbulb ∝ power
• Resistors convert electrical energy to thermal energy
• Temperature of resistor may increase