Electricity: Circuits and their Components – Formula & Equation Sheet
Essential formulas and equations from Curiosity, tailored for Class 7 in Science.
This one-pager compiles key formulas and equations from the Electricity: Circuits and their Components 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 defines the relationship between voltage, current, and resistance in an electrical circuit, helping to solve circuit problems.
Power Formula: P = VI
P represents power (watts), V is voltage (volts), and I is current (amperes). This formula calculates the electrical power consumed by devices, useful in determining energy costs.
Energy Formula: E = Pt
E stands for energy (joules), P is power (watts), and t is time (seconds). This formula relates power consumption to the duration of usage, helping in understanding energy efficiency.
Voltage Divider Rule: Vout = Vin (R2 / (R1 + R2))
Vout is the output voltage, Vin is the input voltage, R1 and R2 are resistances. It calculates the voltage across a specific resistor in a series circuit, useful for designing circuits.
Current in Series: I_total = I1 = I2 = ... = In
In series circuits, the total current is the same through all components. This concept aids in analyzing series circuit problems.
Current in Parallel: I_total = I1 + I2 + ... + In
In parallel circuits, the total current is the sum of the currents through each pathway. Essential for understanding parallel circuit configurations.
Resistance in Series: R_total = R1 + R2 + ... + Rn
R_total is the total resistance, while R1, R2, ... are individual resistances in series. This formula helps calculate net resistance in series circuits.
Resistance in Parallel: 1/R_total = 1/R1 + 1/R2 + ... + 1/Rn
R_total is the total resistance in a parallel circuit. This formula is important for designing complex circuits involving multiple resistors.
Charge: Q = It
Q represents charge (coulombs), I is current (amperes), and t is time (seconds). This concept quantifies the amount of electric charge passing through a circuit.
Electrical Energy: E = QV
E denotes electrical energy (joules), Q is charge (coulombs), and V is voltage (volts). This equation calculates energy transferred when a charge moves through a potential difference.
Equations
Kirchhoff’s Voltage Law: ΣV = 0
This law states that the sum of electrical potential differences (voltage) around a closed circuit is zero. Crucial for analyzing complex circuits.
Kirchhoff’s Current Law: ΣI = 0
The total current entering a junction equals the total current leaving it. It helps in balancing current flow in circuits.
Electric Field: E = F/q
E is the electric field strength (N/C), F is the force (newtons), and q is the charge (coulombs). It describes the force experienced by a charge in an electric field.
Capacitance: C = Q/V
C is capacitance (farads), Q is charge (coulombs), and V is voltage (volts). It defines the ability of a system to store electrical energy.
Induced EMF: ε = -dΦ/dt
ε represents the induced electromotive force (volts), and dΦ/dt is the rate of change of magnetic flux. This describes electromagnetic induction processes.
Power in terms of Resistance: P = I²R
P is power (watts), I is current (amperes), and R is resistance (ohms). This formula calculates power loss in resistors due to current flow.
Energy in terms of Power and Resistance: E = I²Rt
E stands for energy (joules), I is current (amperes), R is resistance (ohms), and t is time (seconds). Useful for assessing energy loss in resistors.
Relationship between Capacitance and Energy: E = 1/2 CV²
Where C is capacitance and V is voltage. It calculates the energy stored in a capacitor, important in electronic circuits.
Equivalent Resistance for Series and Parallel combinations: R_eq = R1 + R2 (Series) / R_eq = 1/(1/R1 + 1/R2) (Parallel)
Used to determine total resistance in circuits depending on how resistors are configured.
Voltage in a Series Circuit: V_total = V1 + V2 + ... + Vn
This equation indicates that total voltage is the sum of voltage drops across each component in series, key for circuit analysis.
