Electrical Formulas

Electricity Formulas (Class 10, 12 & JEE/NEET)

Electricity formulas form the backbone of electrical physics. From basic circuits in Class 10 to complex concepts like Drift Velocity, EMF, and Internal Resistance in Class 12, mastering these formulas is essential for scoring high in CBSE board exams, JEE, and NEET.

Class: 10 & 12
Topic: Current Electricity
Exams: CBSE · JEE · NEET

1. Electric Current and Potential Difference

Electric Current (I) is the rate of flow of electric charge. Potential Difference (V) is the work done in moving a unit charge from one point to another.

Electric Current
I = Qt = n × et
Potential Difference
V = WQ
  • I = Current (Amperes, A)
  • Q = Electric Charge (Coulombs, C)
  • n = Number of electrons, e = Charge of an electron (1.6 × 10-19 C)
  • V = Potential Difference / Voltage (Volts, V)

2. Ohm's Law Formula

Ohm's Law states that the potential difference across a conductor is directly proportional to the current flowing through it, provided physical conditions (like temperature) remain constant.

Ohm's Law
V = I × R

3. Resistance, Resistivity, and Conductance

The resistance of a wire depends on its dimensions and material. Conductance (G) is simply the reciprocal of resistance.

Resistance: R = ρ (L / A)ρ = Resistivity (Ω·m), L = Length, A = Area
Conductance: G = 1 / RS.I. Unit is Siemens (S) or mho (℧).

4. Drift Velocity & Mobility (Class 12 / JEE)

When a voltage is applied, free electrons in a conductor move with an average velocity called Drift Velocity (vd).

Current & Drift Velocity Relation
I = n A e vd
  • vd = Drift velocity (m/s)
  • n = Number density of electrons (electrons per unit volume)
  • A = Cross-sectional area (m2)

Mobility (μ): The magnitude of drift velocity per unit electric field. Formula: μ = vd / E.

5. EMF and Internal Resistance of a Cell

A real battery has some internal resistance (r). The Electromotive Force (E) is the maximum potential difference when no current is drawn.

Terminal Voltage Formula
V = E − Ir

Where V is Terminal Voltage, E is EMF, and I × r is the voltage drop inside the cell. To find the current in a circuit with external resistance R, use: I = E / (R + r).

6. Series and Parallel Combination of Resistors

In Series: Rs = R1 + R2 + R3 + ...Current is the same across all resistors; Voltage divides.
In Parallel: 1Rp = 1R1 + 1R2 + ...Voltage is the same across all branches; Current divides.

7. Electric Power & Joule's Law of Heating

Electric Power Formulas
P = V × I  =  I2R  =  V2R

Joule's Law of Heating: The heat produced by a resistor is given by H = I2Rt. Power is measured in Watts (W) and Heat in Joules (J).

Summary Table of Electricity Formulas & Units

Quantity Formula S.I. Unit
Electric Current I = Q / t Ampere (A)
Potential Difference V = W / Q Volt (V)
Ohm's Law V = IR Volt (V)
Resistance R = ρL / A Ohm (Ω)
Drift Velocity vd = I / (nAe) m/s
Terminal Voltage V = E − Ir Volt (V)
Electric Power P = VI = I2R Watt (W)

Solved Examples on Electricity Formulas

Example 1: Internal Resistance (JEE / NEET Level)

A battery of EMF 12 V and internal resistance 2 Ω is connected to an external resistor. If the current in the circuit is 2 A, what is the value of the external resistance?

Given, EMF (E) = 12 V, Internal Resistance (r) = 2 Ω, Current (I) = 2 A
Formula: I = E / (R + r)
2 = 12 / (R + 2)
R + 2 = 6 ⇒ R = 4
External Resistance = 4 Ω

Example 2: Equivalent Resistance (Class 10)

Two resistors of 10 Ω and 15 Ω are connected in parallel. Find their equivalent resistance.

Given, R1 = 10 Ω, R2 = 15 Ω
Formula: 1 / Rp = (1 / R1) + (1 / R2)
1 / Rp = (1 / 10) + (1 / 15) = (3 + 2) / 30 = 5 / 30 = 1 / 6
Equivalent Resistance (Rp) = 6 Ω

Example 3: Electric Power & Cost

An electric bulb rated 100 W operates for 5 hours a day. Calculate the energy consumed in kWh in 30 days.

Given, Power (P) = 100 W = 0.1 kW
Time per day = 5 hours, Total time (t) = 5 × 30 = 150 hours
Formula: Energy (E) = P × t
E = 0.1 kW × 150 h = 15
Energy Consumed = 15 kWh

Frequently Asked Questions (FAQs)

What is Ohm's Law formula?
Ohm's law formula is V = I × R, where V is the potential difference (Voltage), I is the current, and R is the resistance of the conductor.
How do you calculate drift velocity?
Drift velocity (vd) is calculated using the relation I = nAevd. Rearranging gives vd = I / (nAe), where I is current, n is electron density, A is area, and e is elementary charge.
What is the formula for terminal voltage of a cell?
When a cell is discharging, the terminal voltage is V = E - Ir, where E is the EMF, I is the current, and r is the internal resistance of the cell.
What is the difference between resistance and resistivity?
Resistance (R) is the opposition to current flow in a specific object, and changes with length and area. Resistivity (ρ) is a fundamental property of the material itself and only changes with temperature. The relationship is R = ρL/A.
How do you find total resistance in parallel?
For resistors in parallel, the reciprocal of the total resistance is equal to the sum of the reciprocals of individual resistances: 1/Rp = 1/R1 + 1/R2 + 1/R3 + ...