I = dQ/dt
Current: I = dQ/dt. Conventional current direction. Unit A.
Current
Use when — Conventional current direction. Unit A.
I = n q A v_d
Drift-current magnitude: I = n q A v_d. q is carrier charge magnitude; uniform carrier density and cross-section.
Drift-current magnitude
Use when — q is carrier charge magnitude; uniform carrier density and cross-section.
v_d = mu E in magnitude form
Mobility: v_d = mu E in magnitude form. Low-field linear transport model used at NCERT/NEET depth. mu in m^2 V^-1 s^-1.
Mobility
Use when — Low-field linear transport model used at NCERT/NEET depth. mu in m^2 V^-1 s^-1.
V = IR
Ohm law: V = IR. Ohmic conductor under fixed physical conditions where V-I is linear.
Ohm law
Use when — Ohmic conductor under fixed physical conditions where V-I is linear.
R = rho L/A
Uniform wire: R = rho L/A. Uniform material/cross-section at specified temperature. rho in ohm m.
Uniform wire
Use when — Uniform material/cross-section at specified temperature. rho in ohm m.
sigma = 1/rho
Conductivity: sigma = 1/rho. Linear homogeneous material model. Unit S/m.
Conductivity
Use when — Linear homogeneous material model. Unit S/m.
R = R0[1 + alpha(T-T0)]
Temperature approximation: R = R0[1 + alpha(T-T0)]. Approximate over a range where alpha is effectively constant.
Temperature approximation
Use when — Approximate over a range where alpha is effectively constant.
P = VI; resistor forms I^2R, V^2/R
Electrical power: P = VI; resistor forms I^2R, V^2/R. Steady DC resistor for derived forms. Unit W.
Electrical power
Use when — Steady DC resistor for derived forms. Unit W.
R_eq = sum R_i
Series resistors: R_eq = sum R_i. Same current in ideal series branch.
Series resistors
Use when — Same current in ideal series branch.
1/R_eq = sum 1/R_i
Parallel resistors: 1/R_eq = sum 1/R_i. Same potential difference across branches.
Parallel resistors
Use when — Same potential difference across branches.
V = E - Ir
Discharging cell terminal voltage: V = E - Ir. Current leaves positive terminal; E emf, r internal resistance.
Discharging cell terminal voltage
Use when — Current leaves positive terminal; E emf, r internal resistance.
sum I_in = sum I_out
Kirchhoff junction: sum I_in = sum I_out. Lumped steady circuit.
Kirchhoff junction
Use when — Lumped steady circuit.
algebraic sum of potential changes = 0
Kirchhoff loop: algebraic sum of potential changes = 0. Use one traversal direction and consistent source/resistor signs.
Kirchhoff loop
Use when — Use one traversal direction and consistent source/resistor signs.
P/Q = R/S
Wheatstone balance: P/Q = R/S. Balance condition with named four-arm layout and zero galvanometer current.
Wheatstone balance
Use when — Balance condition with named four-arm layout and zero galvanometer current.
R_left/R_right = l/(100-l)
Metre bridge: R_left/R_right = l/(100-l). At balance for uniform bridge wire; exact ratio depends on diagram assignment.
Metre bridge
Use when — At balance for uniform bridge wire; exact ratio depends on diagram assignment.