Current Electricity
Complete Formula Sheet & Shortcut Bible · BITSAT 2026
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Fundamental Concepts & Ohm's Law
Electric Current
I = dQ/dt = neAvₐ
Rate of flow of charge. A is cross-section area, vₐ is drift velocity.
Current Density
J = I/A = σE
Vector form of Ohm's Law. σ is conductivity.
Drift Velocity
vₐ = (eE/m)τ
Average velocity of electrons. τ is relaxation time.
Ohm's Law
V = IR
Potential difference is proportional to current for ohmic conductors.
Resistance
R = ρL/A
ρ is resistivity, L is length, A is cross-section area.
Conductance & Conductivity
G = 1/R
σ = 1/ρ
σ = 1/ρ
Reciprocals of resistance and resistivity respectively.
Temperature Dependence & Heating
Resistance & Temperature
Rₜ = R₀[1 + α(T - T₀)]
α is the temperature coefficient of resistance.
Resistivity & Temperature
ρₜ = ρ₀[1 + α(T - T₀)]
For conductors, α is positive. For semiconductors, α is negative.
Joule's Law of Heating
H = I²Rt
Heat produced in a resistor. Unit is Joules (J).
Electric Power
P = VI = I²R = V²/R
Rate at which electrical energy is consumed. Unit is Watts (W).
Cells & EMF
EMF & Internal Resistance
V = E - Ir
V is terminal voltage, E is EMF, r is internal resistance. V > E during charging.
Cells in Series
Eₑₙ = ΣEᵢ
rₑₙ = Σrᵢ
rₑₙ = Σrᵢ
For n identical cells: Eₑₙ = nE, rₑₙ = nr.
Cells in Parallel
Eₑₙ/rₑₙ = Σ(Eᵢ/rᵢ)
1/rₑₙ = Σ(1/rᵢ)
1/rₑₙ = Σ(1/rᵢ)
For n identical cells: Eₑₙ = E, rₑₙ = r/n.
Maximum Power Transfer
Pₘₐₓ = E² / 4R
when R = r
when R = r
Max power is delivered to external resistance R when it equals internal resistance r.
Kirchhoff's Laws & Circuit Analysis
Kirchhoff's Current Law (KCL)
ΣI = 0 at a junction
Also called the Junction Rule. Based on conservation of charge.
Kirchhoff's Voltage Law (KVL)
ΣΔV = 0 in a closed loop
Also called the Loop Rule. Based on conservation of energy.
BITSAT Circuit Solvers
For symmetric circuits (e.g., cube), use symmetry lines. Points on a line of symmetry are at the same potential and can be joined or separated.
If a wire is stretched to 'n' times its original length, its new resistance becomes R' = n²R, as volume (AL) is constant.
In a balanced Wheatstone Bridge (R₁/R₂ = R₃/R₄), the galvanometer current is zero. The middle resistor can be removed for simplification.
Use Nodal Analysis (KCL) for circuits with fewer nodes than loops. It's often faster than KVL.
For infinite ladder problems, assume the equivalent resistance of the entire ladder is X. Add one more repeating section to X, and the total should still be X. Solve the resulting quadratic equation.
Measuring Instruments
Wheatstone Bridge
P/Q = R/S
Condition for a balanced bridge. No current flows through the galvanometer.
Meter Bridge
R/S = l₁ / (100 - l₁)
Practical form of Wheatstone bridge. l₁ is the balancing length.
Potentiometer Principle
V ∝ L
Potential drop across a uniform wire is proportional to its length.
Compare EMFs
E₁/E₂ = l₁/l₂
Using a potentiometer, where l₁ and l₂ are balancing lengths for cells E₁ and E₂.
Find Internal Resistance
r = R (l₁/l₂ - 1)
R is shunt resistance. l₁ is length without shunt, l₂ is with shunt.
Resistor Combinations at a Glance
| Parameter | Series Combination | Parallel Combination |
|---|---|---|
Equivalent Resistance | Rₑₙ = R₁ + R₂ + ... | 1/Rₑₙ = 1/R₁ + 1/R₂ + ... |
Current | Same through each resistor (I) | Divides (I = I₁ + I₂ + ...) |
Voltage | Divides (V = V₁ + V₂ + ...) | Same across each resistor (V) |
Voltage Divider Rule | Vₓ = Vₜₒₜₐₗ (Rₓ / Rₑₙ) | N/A |
Current Divider Rule | N/A | Iₓ = Iₜₒₜₐₗ (Rₑₙ / Rₓ) |