Electricity is a branch of physics that deals with the study of electric charges, currents, and fields. It is an important chapter in science that is studied in class 10. Here is a detailed explanation of the formulas and derivation of the electricity chapter.

Electric current and circuits:
- Electric current is the flow of electric charge through a conductor.
- It is measured in amperes (A) and is given by the formula, I = Q/t, where I is the electric current, Q is the charge and t is the time taken.
- The unit of charge is coulombs (C).
- The direction of the flow of electric current is taken as the direction of the flow of positive charge.

Ohm's law:
- Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points.
- It is given by the formula, V = IR, where V is the voltage, I is the current, and R is the resistance of the conductor.
- The unit of resistance is ohms (Ω).

Series and parallel circuits:
- In a series circuit, the components are connected one after the other, and the same current flows through each component.
- The total resistance in a series circuit is given by the formula, R = R1 + R2 + ... + Rn, where R is the total resistance, and R1, R2, ... Rn are the resistances of individual components.
- In a parallel circuit, the components are connected in parallel to each other, and the voltage across each component is the same.
- The total resistance in a parallel circuit is given by the formula, 1/R = 1/R1 + 1/R2 + ... + 1/Rn, where R is the total resistance, and R1, R2, ... Rn are the resistances of individual components.

Electric power:
- Electric power is the rate at which electrical energy is transferred by an electric circuit.
- It is given by the formula, P = VI, where P is the power, V is the voltage, and I is the current.
- The unit of power is watts (W).

Electromagnetic induction:
- Electromagnetic induction is the process of generating an electromotive force (EMF) in a conductor by varying the magnetic field around it.
- Faraday's law of electromagnetic induction states that the EMF induced in a conductor is directly proportional to the rate of change of magnetic flux.
- It is given by the formula, EMF = -dΦ/dt, where EMF is the electromotive force, Φ is the magnetic flux, and t is the time taken.
- The minus sign in the formula represents Lenz's law, which states that the direction of the induced EMF is such that it opposes the change that caused it.

Conclusion:
Electricity is a fascinating subject that has many practical applications in our daily lives. Understanding the formulas and derivation of the electricity chapter is essential for students studying in class 10. By mastering this chapter, students can develop a strong foundation in electrical concepts that can help them in their future studies and careers.