Electricity: Magnetic and Heating Effects – Formula & Equation Sheet
Essential formulas and equations from Curiosity, tailored for Class 8 in Science.
This one-pager compiles key formulas and equations from the Electricity: Magnetic and Heating Effects chapter of Curiosity. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Key concepts & formulas
Essential formulas, key terms, and important concepts for quick reference and revision.
Formulas
Ohm’s Law: V = IR
V is voltage (volts), I is current (amperes), and R is resistance (ohms). This law states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points.
Power: P = VI
P is power (watts), V is voltage (volts), and I is current (amperes). This formula helps calculate the power consumed in an electrical circuit, which is crucial for understanding energy usage.
Heat produced: H = I²Rt
H is heat (joules), I is current (amperes), R is resistance (ohms), and t is time (seconds). This equation represents the heating effect of electric current in a conductor.
Magnetic Field (B): B = μ₀(I/2πr)
B is magnetic field (teslas), μ₀ is the permeability of free space (4π × 10⁻⁷ T·m/A), I is current (A), and r is the distance from the wire (meters). This formula describes the strength of the magnetic field around a straight current-carrying wire.
Electromagnet Strength: F = BIL
F is the force (newtons), B is the magnetic field strength (teslas), I is current (amperes), and L is the length of wire in the magnetic field (meters). It calculates the force acting on a wire carrying current in a magnetic field.
Voltage Drop: V = L × R
V is the voltage drop (volts), L is the length of the conductor (meters), and R is the resistance per unit length (ohms per meter). This is important for calculating losses in long electrical circuits.
Total Resistance in Series: R_total = R₁ + R₂ + ... + R_n
R_total is the total resistance (ohms) in a series circuit. This formula is used for finding the equivalent resistance when resistors are connected end-to-end.
Total Resistance in Parallel: 1/R_total = 1/R₁ + 1/R₂ + ... + 1/R_n
R_total is the total resistance (ohms) in a parallel circuit. It helps determine how combined resistors affect the circuit's overall resistance.
Capacitance: C = Q/V
C is capacitance (farads), Q is charge (coulombs), and V is voltage (volts). This formula describes how much charge a capacitor can store per unit voltage.
Energy Stored in a Capacitor: E = ½ CV²
E is energy (joules), C is capacitance (farads), and V is voltage (volts). This formula calculates the amount of electrical energy stored in a capacitor.
Equations
Fleming's Left-Hand Rule: F, I, B are mutually perpendicular
F is the direction of force, I is the direction of current, and B is the direction of the magnetic field. This rule is used to find the direction of force on a current-carrying conductor in a magnetic field.
Faraday’s Law of Electromagnetic Induction: ε = -dΦ/dt
ε is induced electromotive force (volts) and dΦ/dt is the rate of change of magnetic flux (weber/second). This law describes how a changing magnetic field can induce an electric current.
Voltage in a Circuit: V = IR + V_r
V is the total voltage (volts), IR is the voltage across a resistor in a series circuit, and V_r is any other voltage drops in the circuit.
Kirchhoff’s First Law: ΣI_in = ΣI_out
This states that the total current entering a junction equals the total current leaving the junction. It's fundamental for analyzing complex circuits.
Kirchhoff’s Second Law: ΣV = 0
The sum of the electromotive forces in any closed loop is equal to the sum of the potential drops in that loop. This aids in circuit analysis.
Battery Voltage: V = E – Ir
V is the terminal voltage (volts), E is the electromotive force (volts), I is current (amperes), and r is the internal resistance of the battery (ohms). It helps understand battery performance under load.
Induced EMF in a Loop: ε = -dΨ/dt
ε is induced electromotive force (volts), dΨ is the change in magnetic flux (webers), and dt is change in time (seconds). Used to describe induced voltage in a coil cut by a magnetic field.
Power in Circuits: P = E/t
P is power (watts), E is energy transferred (joules), and t is time (seconds). This equation indicates power as energy per unit time.
Resistance: R = ρ(L/A)
R is resistance (ohms), ρ is resistivity (ohm-meters), L is length (meters), and A is cross-sectional area (square meters). It relates physical properties of materials to resistance.
Circuit Analysis: V = IR total
In any circuit, the voltage across the entire circuit equals the total current multiplied by the total resistance. This is used for solving circuit problems.
