🔌 Current Electricity – Ohm’s Law & Circuits

Current, drift, resistivity, Ohm’s law, cells, bridges, potentiometer, Joule heating, RC time

I = Q/t R = ρL/A V = IR τ = RC
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💡 Current electricity at a glance

Electric current I = Q/t flows when charge moves through a conductor; at microscopic level electrons drift with v_d so that I = n e A v_d. Resistance R = ρ L/A depends on material (resistivity ρ) and geometry. Ohm’s law V = IR holds for ohmic conductors. Cells have EMF ε and internal resistance r; circuits obey Kirchhoff’s current and voltage laws. RC circuits charge/discharge with time constant τ = RC, and Joule’s law H = I² R t describes heating.

Current electricity calculators

Microscopic current, Ohm’s law, cells, bridges, potentiometer, heating & RC

Current from charge and time (I = Q/t)
Current density and drift (J, v_d)
Resistance, resistivity, conductivity (R, ρ, σ)
I = —, J = —, v_d = —, ρ = —, σ = —
I = Q/t, J = I/A, v_d = I/(n e A), ρ = R A/L, σ = 1/ρ.
Ohm’s law (any two → third)
Wire resistance (R = ρL/A)
Temperature dependence (R = R₀ (1 + αΔT))
V = —, I = —, R = —, R_wire = —, R(T) = —
Uses V = IR, R = ρL/A, and R = R₀ (1 + αΔT).
Single cell with external resistance (ε, r, R)
Identical cells in series/parallel (n, ε, r)
I = —, V_term = —, P_load = —, (ε_eq, r_eq, I_batt) = —
Single: I = ε/(R+r), V_term = ε − Ir, P = I²R. For n identical cells: series ε_eq = nε, r_eq = nr; parallel ε_eq = ε, r_eq = r/n.
Balanced Wheatstone bridge (P, Q, R → S)
Meter bridge (slide wire): R, l₁, l₂ → X
Potentiometer: comparison & internal resistance
S = —, X = —, k = —, ε₁/ε₂ = —, r = —
Bridge: P/Q = R/S. Meter bridge: R/X = l₁/l₂. Potentiometer: k = V/L, ε₁/ε₂ = l₁/l₂, r = R(l₁ − l₂)/l₂.
Joule heating (H = I² R t)
RC time constant (τ = RC) and key times
H = —, τ = —, charging/discharging values listed below
Shows Joule heat H and τ, plus approximate V_C(t) for charging/discharging at t = τ, 2τ, 3τ, 5τ.

📈 Current electricity graph

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Basic current electricity quantities & definitions

Quantity Symbol / Formula SI unit Notes
Electric current I = Q / t A (ampere) Rate of flow of charge
Current density J = I / A A/m² Vector, direction of conventional current
Drift velocity I = n e A v_d ⇒ v_d = I / (n e A) m/s Average slow drift of electrons
Resistance R = V / I Ω Opposition to current
Resistivity & conductivity R = ρ L / A, σ = 1/ρ ρ: Ω·m, σ: S/m Material properties

Ohm’s law, cells, bridges, potentiometer, heating & RC

Concept Formula Notes
Ohm’s law V = I R Ohmic conductors at constant temperature
Temperature dependence R = R₀ (1 + αΔT) α = temperature coefficient
Series & parallel R_s = ΣRᵢ, 1/R_p = Σ(1/Rᵢ) Current same in series, voltage same in parallel
Cell with internal resistance I = ε / (R + r), V_term = ε − I r P_load = I²R, max when R = r
Wheatstone bridge P/Q = R/S (balanced) No galvanometer current at balance
Meter bridge R/X = l₁/l₂ l₁ + l₂ = 100 cm
Potentiometer k = V/L, ε₁/ε₂ = l₁/l₂, r = R(l₁ − l₂)/l₂ Null deflection method (no current from test cell)
Joule heating H = I² R t Heat produced in resistor
RC circuit τ = R C Charging: V_C = ε(1 − e^{−t/τ}); discharging: V = V₀ e^{−t/τ}

About this current electricity tool

This page organizes the main current electricity formulas used in school physics, JEE, and NEET: microscopic current and drift, resistivity and conductivity, Ohm’s law and combinations, cells with internal resistance and power transfer, Wheatstone/meter bridge, potentiometer, Joule heating, and RC time constant. Each calculator is paired with step-by-step reasoning to connect formulas to physical intuition.