Calculate the resonant frequency of an LC circuit — essential for filters, oscillators, and tuning circuits. "The natural frequency at which an LC circuit stores and exchanges energy between magnetic and electric fields." Key Formula: Resonant Frequency f 0 = 1 / (2 π √ LC ) Where: f 0 : Resonant frequency (Hz) L : Inductance (H) C : Capacitance (F) Note : This formula applies to both series and parallel LC circuits. Parameter Definitions 1. Inductance (L) The value of inductance in the circuit, measured in henrys (H). It represents the coil’s ability to store energy in a magnetic field. Practical units : • Microhenry (μH) = 10⁻⁶ H • Millihenry (mH) = 10⁻³ H • Henry (H) – used for large inductors Example : A ferrite core inductor may have 10 μH 2. Capacitance (C) The value of capacitance in the circuit, measured in farads (F). It represents the capacitor’s ability to store charge. Practical units : • Picofarad (pF) = 10⁻¹² F • Nanofarad (nF) = 10⁻⁹ F • Microfarad (μF) = 10⁻⁶ F • Farad (F) – rarely used in practice Example : A ceramic capacitor may have 100 pF How It Works At resonance: Inductive reactance equals capacitive reactance (X L = X C ) The circuit oscillates naturally without external driving force Solving for $ f $ gives the resonant frequency formula In a series LC circuit : • Impedance is minimum → current is maximum • Used in band-pass filters and oscillators In a parallel LC circuit : • Impedance is maximum → voltage is maximum • Used in tank circuits and antenna tuning Energy continuously swaps between the inductor (magnetic field) and capacitor (electric field), creating sustained oscillations. Application Scenarios Tuning radio receivers to specific stations Designing band-pass and band-stop filters Building oscillators (e.g., crystal, Hartley, Colpitts) Matching antennas to transmitter frequencies Power electronics (resonant converters) Teaching AC circuit theory in classrooms

Calculate output voltage using the voltage divider rule — essential for electronics design. "A circuit that reduces voltage by dividing it across two resistors in series." Key Principle: Voltage Divider Rule \( V_{out} = V_{in} \cdot \frac{R_2}{R_1 + R_2} \) Where: V in : Input voltage (V) V out : Output voltage (V) R 1 , R 2 : Resistance values (Ω) Note : Voltage divides proportionally with resistance — higher resistance gets more voltage. Parameter Definitions 1. Input Voltage (V in ) The total voltage supplied to the circuit, measured in volts (V). Example: 5 V from a battery or power supply 2. Output Voltage (V out ) The voltage dropped across resistor R 2 , which is the desired output. This is commonly used to provide reference voltages for sensors, microcontrollers, or amplifiers. 3. Resistor Ratio (R₁/R₂) The ratio of the two series resistances. This determines how the voltage is divided. Examples : • If R₁ = R₂ → V out = V in /2 • If R₂ ≫ R₁ → V out ≈ V in • If R₁ ≫ R₂ → V out ≈ 0 How It Works When resistors are connected in series : They share the same current Voltage divides across each resistor Total voltage: V in = V₁ + V₂ Current: I = V in / (R₁ + R₂) Voltage across R₂: V out = I × R₂ Application Scenarios Providing reference voltages for analog circuits Scaling down sensor signals (e.g., thermistors, potentiometers) Biasing transistors and operational amplifiers Creating adjustable voltage sources Teaching basic circuit theory in classrooms

Calculate output current in parallel circuits using the current divider rule. "A circuit that produces an output current proportional to the input, based on resistor ratios." Key Principle: Current Divider Rule ( I_1 = I \cdot \frac{R_2}{R_1 + R_2} \quad \text{and} \quad I_2 = I \cdot \frac{R_1}{R_1 + R_2} ) Where: I : Total input current (A) I 1 : Current through R 1 I 2 : Current through R 2 R 1 , R 2 : Resistance values (Ω) Note : Current divides inversely with resistance — higher resistance draws less current. Parameter Definitions 1. Input Current (I) The total current entering the parallel network, measured in amperes (A). Example: 10 A from a power supply 2. Output Current (I₁/I₂) The current flowing through one of the parallel resistors. - I₁ : Current through R₁ - I₂ : Current through R₂ 3. Resistor Ratio (R₁/R₂) The ratio of the two parallel resistances. This determines how the current is divided. Examples : • If R₁ = R₂ → I₁ = I₂ = I/2 • If R₁ > R₂ → I₁ < I₂ How It Works When resistors are connected in parallel : They share the same voltage Total current splits between branches Current is inversely proportional to resistance Equivalent resistance: \( \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} \) Application Scenarios Designing sensor biasing circuits Creating adjustable current sources Analyzing multi-path power distribution Teaching basic circuit theory Debugging parallel load behavior

Calculate inductive and capacitive reactance in AC circuits. "The opposition caused by inductance or capacitance to alternating current." Types of Reactance Inductive Reactance (X L ) : Opposition from inductors to AC current Capacitive Reactance (X C ) : Opposition from capacitors to AC current Key Formulas ( X_L = 2\pi f L \) \( X_C = \frac{1}{2\pi f C} \) Where: X L : Inductive reactance (Ω) X C : Capacitive reactance (Ω) f : Frequency (Hz) L : Inductance (H) C : Capacitance (F) Note : \( X_L \) increases with frequency; \( X_C \) decreases with frequency. Parameter Definitions 1. Inductive Reactance (X L ) The opposition an inductor presents to AC current flow. Energy is stored in a magnetic field, causing current to lag voltage by 90°. Common in motors, transformers, and chokes. 2. Capacitive Reactance (X C ) The opposition a capacitor presents to AC current flow. Energy is stored in an electric field, causing current to lead voltage by 90°. Common in filters, power factor correction, and coupling circuits. 3. Frequency (f) The number of cycles per second in an AC waveform, measured in hertz (Hz). Standard power frequencies : • 50 Hz – Used in most countries (e.g., China, Europe) • 60 Hz – Used in North America, Japan 4. Inductance (L) A measure of a coil's ability to store energy in a magnetic field. Unit: Henry (H) . Practical units : • Microhenry (μH) = 10⁻⁶ H • Millihenry (mH) = 10⁻³ H 5. Capacitance (C) A measure of a capacitor's ability to store charge. Unit: Farad (F) . Practical units : • Microfarad (μF) = 10⁻⁶ F • Nanofarad (nF) = 10⁻⁹ F • Picofarad (pF) = 10⁻¹² F Application Scenarios Designing LC filters and tuned circuits Calculating resonant frequency in RLC circuits Analyzing phase relationships in AC systems Teaching AC circuit fundamentals Troubleshooting motor or power factor issues

Power factor correction (PFC) is a technique that improves the efficiency of an electrical system by adding capacitors to offset the reactive power generated by inductive loads (e.g., motors, transformers). This reduces current draw, minimizes energy losses, and lowers utility bills. This tool calculates the required capacitor capacity (in kVAR) to raise the power factor from its current value to a desired level. Commonly used in industrial plants, commercial buildings, data centers, and other facilities with significant inductive loads. Parameter Description Parameter Description Voltage Operating voltage of the system. • Single-phase: Enter **Phase-Neutral voltage** • Two-phase / Three-phase: Enter **Phase-Phase voltage** Frequency Number of cycles per second, unit: Hertz (Hz). Typically 50 Hz or 60 Hz Load Active power consumed by the load, unit: kilowatts (kW) Current Power Factor Existing power factor value between 0 and 1. For example, 0.7 indicates low efficiency Desired Power Factor Target power factor after correction. Must be higher than the initial value. Recommended: ≥ 0.95 Capacitor Voltage Rated voltage of the capacitor bank. Must match system voltage (e.e., 400V, 415V) Connection Type Configuration of the capacitor bank: • Star (Y): Suitable for high-voltage or balanced three-phase systems • Delta (Δ): Common for low-voltage or high-current applications Calculation Principle The required reactive power compensation (Qc) is calculated using: Q_c = P × (tanφ₁ - tanφ₂) Where: - Q_c: Required capacitor capacity (kVAR) - P: Load active power (kW) - φ₁: Initial phase angle, where cosφ₁ = PF₁ - φ₂: Target phase angle, where cosφ₂ = PF₂ Example: For a 100 kW load with initial PF = 0.7 and target PF = 0.95, approximately 58 kVAR of capacitance is needed. Usage Recommendations Monitor power factor regularly and use automatic switching capacitor banks Select capacitors with appropriate rated voltage to prevent overvoltage or under-voltage operation Use step-controlled capacitor banks for dynamic compensation Avoid over-correction, which may cause capacitive conditions, resonance, or voltage rise Combine with power quality analyzers for real-time data and improved accuracy

What is Impedance? Impedance is the total opposition a circuit offers to the flow of alternating current (AC). It combines resistance (R) and reactance (X), and is measured in ohms (Ω). “The opposition of a circuit to the passage of an alternating electric current.” Key Parameters Resistance (R) The inherent opposition to electric current due to the material's properties. It dissipates energy in the form of heat. “The tendency of a body to oppose the passage of an electric current.” Reactance (X) The opposition caused by inductance (L) or capacitance (C) in AC circuits. Unlike resistance, reactance stores and releases energy rather than dissipating it. “Opposition presented to alternating current by inductance or capacitance.” How It Works Use this calculator to compute impedance (Z) using the formula: ( Z = sqrt{R^2 + X^2} ) Where: Z : Impedance (in Ω) R : Resistance (in Ω) X : Reactance (in Ω) Use Case Ideal for electrical engineers, students, and technicians working with AC circuits — quickly calculate impedance without manual math.

Capacitor Power at Different Voltage In certain power networks, a significant difference may exist between the rated voltage and the service voltage. For example, a capacitor rated at 400 V may be used in a 380 V system. In such cases, the actual reactive power output of the capacitor varies with voltage and frequency. This tool calculates the real reactive power delivered by a capacitor under non-rated conditions. Application Scenarios Industrial substation reactive power compensation Capacitor bank selection verification System voltage fluctuation analysis Capacitor lifespan evaluation (overvoltage/undervoltage) Parameter Description Parameter Description Input Voltage Actual operating voltage of the network (e.g., 380V, 400V), unit: Volts (V) Supply Frequency Operating frequency of the network (e.g., 50 Hz or 60 Hz), unit: Hertz (Hz) Capacitor Rated Power Nominal reactive power rating of the capacitor, unit: kVAR Capacitor Rated Voltage Rated voltage specified on the capacitor nameplate, unit: Volts (V) Capacitor Rated Frequency Design frequency of the capacitor, typically 50 Hz or 60 Hz Calculation Principle The reactive power output of a capacitor is proportional to the square of the applied voltage: Q_actual = Q_rated × (U_in / U_rated)² × (f_supply / f_rated) Where: - Q_actual: Actual reactive power output (kVAR) - Q_rated: Rated reactive power of the capacitor (kVAR) - U_in: Input voltage (V) - U_rated: Rated voltage of the capacitor (V) - f_supply: Supply frequency (Hz) - f_rated: Rated frequency of the capacitor (Hz) A 10% increase in voltage results in approximately 21% higher reactive power (due to quadratic relationship) Overvoltage can cause overheating, insulation breakdown, or reduced lifespan Usage Recommendations Avoid long-term operation above the capacitor's rated voltage Select capacitors with slightly higher rated voltage than system voltage (e.g., 400V for 380V systems) Use step-by-step switching in multi-level capacitor banks to prevent overcompensation Combine with power factor controllers for dynamic reactive power management

This tool calculates the grounding resistance of an earthing system based on soil resistivity, electrode type, and geometric parameters. It helps verify compliance with IEC 60364-4-41 for coordination between earth electrodes and residual current devices (RCBOs). The calculated resistance is compared to the safety voltage limit (typically 50 V or 25 V) to ensure safe operation and proper tripping of protective devices. Input Parameters: • Type of ground electrode – Physical form of the grounding element: - Rod - Horizontal rope - Ring - Mesh network • Soil Type – The type of soil where the electrode is installed. Used to estimate resistivity (ρ). Typical values: - Agricultural: 10–150 Ω·m - Sandy gravelly: 50–300 Ω·m - Clay: 50–200 Ω·m - Marine sands: 200–3000 Ω·m - Rocky: 1500–10000 Ω·m - Custom: User-defined value • Quantity (n) – Number of parallel grounding electrodes used. • Length (L) – Total length of the grounding conductor in meters. - For Rod: depth of the vertical rod - For Horizontal rope: total length of the conductor - For Ring: circumference of the ring - For Mesh network: total length of all buried conductors • Resistivity (ρ) – Soil resistivity in ohm-meters (Ω·m). If not measured, use typical values from soil type. • Safety Voltage – Maximum allowable touch voltage: - 50 V: Normal dry environments - 25 V: Wet, confined, or high-risk locations Usage Tip: Enter the parameters and calculate the grounding resistance. Then check if: R ≤ U₀ / IΔn Where: R = Ground resistance (Ω) U₀ = Safety voltage (50 V or 25 V) IΔn = Rated residual operating current of RCBO (e.g., 0.03 A for 30 mA) Example: For 30 mA RCBO and 50 V safety limit: R ≤ 50 / 0.03 ≈ 1667 Ω → System is acceptable if R < 1667 Ω.

Calculate voltage in DC and AC circuits using key electrical parameters. "Difference in electric potential between two points." Key Parameters Current Type Direct Current (DC) : Current flows constantly from positive to negative pole. Used in batteries, solar panels, and electronics. Alternating Current (AC) : Current reverses direction and amplitude over time at a constant frequency (e.g., 50 Hz or 60 Hz). Used in power grids and homes. System Types: Single-phase : One phase conductor and one neutral. Two-phase : Two phase conductors (rare). Three-phase : Three phase conductors; four-wire includes neutral. Current (I) Flow of electric charge through a material, measured in amperes (A). In AC circuits, current may have a phase shift relative to voltage. Active Power (P) Real power that is actually consumed by a load, measured in watts (W). Formula: P = V × I × cosφ Example: A heater converts active power into heat. Reactive Power (Q) Power that alternately flows in reactance without being transformed into other forms of energy, measured in VAR. Formula: Q = V × I × sinφ Apparent Power (S) Total power flowing in the circuit, combining active and reactive components, measured in VA. Formula: S = V × I Relationship: S² = P² + Q² Power Factor (PF) Ratio of active power to apparent power: PF = cosφ, where φ is the phase angle between voltage and current. Resistance (R) Tendency of a body to oppose the passage of electric current, measured in ohms (Ω). Applies to DC circuits and AC resistive loads. Ohm’s Law: V = I × R Impedance (Z) Opposition of a circuit to alternating current, measured in ohms (Ω). Includes resistance and reactance: Z = √(R² + X²) In AC circuits: V = I × Z Key Formulas (Pure HTML) V = I × R V = P / I V = √(P × R) V = I × Z Application Scenarios Designing power supplies and converters Troubleshooting voltage drops in wiring Calculating transformer ratings Improving power factor in industrial plants Analyzing efficiency of electrical systems Educational tools for physics and engineering students

Calculate voltage drop in DC and AC circuits using key electrical parameters. "Voltage drop is the decrease of electrical potential along the path of a current flowing in an electrical circuit. According to Annex G – IEC 60364–5–52." Key Parameters Current Type Direct Current (DC) : Current flows constantly from positive to negative pole. Used in batteries, solar panels, and electronics. Alternating Current (AC) : Current reverses direction and amplitude over time at a constant frequency (e.g., 50 Hz or 60 Hz). Used in power grids and homes. System Types: Single-phase : One phase conductor and one neutral. Two-phase : Two phase conductors (rare). Three-phase : Three phase conductors; four-wire includes neutral. Unipolar : One conductor. Bipolar : Two conductors. Tripolar : Three conductors. Quadrupolar : Four conductors. Pentapolar : Five conductors. Multipolar : Two or more conductors. Operating Temperature Permissible operating temperature depending on the conductor insulation material. IEC/CEI: 70°C (158°F): PVC insulation, PVC-coated mineral insulation, or accessible bare mineral insulation. 90°C (194°F): XLPE, EPR, or HEPR insulation. 105°C (221°F): Bare and non-accessible mineral insulation. NEC: 60°C (140°F): Types TW, UF 75°C (167°F): RHW, THHW, THW, THWN, XHHW, USE, ZW 90°C (194°F): TBS, SA, SIS, FEP, FEPB, MI, RHH, RHW-2, THHN, THHW, THW-2, THWN-2, USE-2, XHH, XHHW, XHHW-2, ZW-2 Phase Conductors in Parallel Conductors of the same cross-sectional area, length, and material can be connected in parallel. The maximum permissible current is the sum of the individual-core maximum currents. Line Length Distance between supply point and load (one way), measured in meters or feet. Longer lines result in higher voltage drop. Conductor Material used for the conductor. Common materials include copper (lower resistance) and aluminum (lighter, cheaper). Cable Type Defines the number of conductors in the cable: Unipolar : One conductor Bipolar : Two conductors Tripolar : Three conductors Quadrupolar : Four conductors Pentapolar : Five conductors Multipolar : Two or more conductors Voltage Difference in electric potential between two points. Enter Phase-Neutral voltage for single-phase systems (e.g., 120V). Enter Phase-Phase voltage for two-phase or three-phase systems (e.g., 208V, 480V). Load Power to be considered for determining circuit characteristics, measured in watts (W) or kilowatts (kW). Includes all connected devices. Power Factor (PF) Ratio of active power to apparent power: cosφ, where φ is the phase angle between voltage and current. Value ranges from 0 to 1. Ideal = 1 (purely resistive load). Wire Size Cross-sectional area of the conductor, measured in mm² or AWG. Larger size → lower resistance → less voltage drop. Key Formulas (Pure HTML) VD = I × R × L VD (%) = (VD / V) × 100 R = ρ × L / A Application Scenarios Designing electrical installations in buildings Sizing wires for long-distance power transmission Troubleshooting dim lights or motor issues Compliance with IEC 60364 and NEC standards Industrial plant planning Renewable energy systems (solar, wind)