Current Electricity — Formula Sheet

For steady current

I = q/t, where q is the net charge flowing in time t.

For non-steady (instantaneous) current

I(t) = lim(ΔQ/Δt) as Δt → 0, which is the derivative dQ/dt.

Ohm's Law

V ∝ I, or V = IR, where R is the resistance of the conductor.

Resistance R depends on the material and dimensions of the conductor: R = ρl/A.

For metals, resistivity increases with temperature

ρ_T = ρ₀[1 + α(T - T₀)]

Physical reason

As temperature increases, τ (relaxation time) decreases due to more frequent collisions, so ρ = m/(ne²τ) increases.

Electric current (I) is defined as the net charge flowing across a cross-section per unit time: I = ΔQ/Δt (in amperes, A).

Power dissipated is P = VI = I²R = V²/R (in watts).