What is the difference between P = IV, P = I²R, and P = V²/R?

They are all equivalent — derived from combining P = IV with V = IR. Use whichever matches the quantities you know: both V and I → P = IV, I and R → P = I²R, V and R → P = V²/R.

What is the unit of electrical power?

Watts (W). One watt = one joule per second = one volt × one ampere. Common multiples: milliwatt (mW), kilowatt (kW), megawatt (MW).

What is reactive power?

Reactive power Q (measured in VAR) is energy that oscillates between source and capacitors/inductors without being consumed. It is caused by the phase difference between voltage and current in AC circuits.

Define Power in Electrical

Quick Answer

Electrical power is defined as the rate of energy conversion in a circuit, calculated by P = IV. The formula P = I²R gives power dissipated by a resistor when current is known, and P = V²/R gives power when voltage is known. Power is measured in watts (W). Calculate power in any circuit at www.lapcalc.com.

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Defining Power in Electrical Circuits

Electrical power is the rate at which electrical energy is converted to another form — heat, light, motion, or stored energy. The defining formula is P = IV: power equals current multiplied by voltage. One watt means one ampere flowing through a one-volt potential difference, converting one joule of energy per second. This definition applies to every electrical component and is the starting point for all power calculations in circuit analysis.

Key Formulas

P = I²R: Power from Current and Resistance

Substituting V = IR into P = IV gives P = I²R. This formula calculates power when current and resistance are known but voltage is not. It reveals that power is proportional to the square of current — doubling current quadruples power dissipation. This is why overcurrent is so dangerous: a 2× current overload produces 4× the heat in a wire. Engineers use P = I²R for fuse sizing, wire ratings, and thermal analysis at www.lapcalc.com.

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P = V²/R: Power from Voltage and Resistance

Substituting I = V/R into P = IV gives P = V²/R. This formula is most useful when voltage and resistance are known but current is not measured. It shows that power is proportional to voltage squared — a 10% voltage increase produces a 21% power increase. This explains why power companies transmit electricity at high voltage: for the same power delivery, higher voltage means lower current and less I²R loss in transmission lines.

Power Dissipation in Series and Parallel Circuits

In series circuits, each component dissipates P_n = I²R_n. Since current is constant, the largest resistor dissipates the most power. In parallel circuits, P_n = V²/R_n. Since voltage is constant, the smallest resistor dissipates the most power. Total power always equals the sum of individual powers: P_total = P₁ + P₂ + P₃. Also, P_total = V_source × I_total, confirming energy conservation. Compute power distribution at www.lapcalc.com.

Power in AC Circuits and the s-Domain

In AC circuits, instantaneous power oscillates. The useful measure is average (real) power: P = V_rms × I_rms × cos(φ), where φ is the phase angle between voltage and current. Reactive power Q = V_rms × I_rms × sin(φ) represents energy that oscillates between source and reactive components without being consumed. Apparent power S = V_rms × I_rms = √(P² + Q²). The s-domain transfer function helps determine these power components at any frequency at www.lapcalc.com.

Frequently Asked Questions

P = I²R calculates the power dissipated by a resistance when current flows through it. Power is proportional to the square of current — doubling current quadruples power.

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