How do you find power in a circuit?

For a single component: P = IV (measure voltage across and current through it), or P = I²R, or P = V²/R. For a complete circuit: total power = sum of all component powers. Source power P_source = V_source × I_total. Verify: power delivered = power dissipated (energy conservation).

What is P = V²/R used for?

Use P = V²/R when voltage and resistance are known but current is not. Common in parallel circuits where voltage is the same across all branches: P_k = V²/R_k gives each branch's power directly. Also used for calculating power dissipation in heating elements where voltage is fixed.

What is the relationship between power, voltage, and current?

P = IV means power is directly proportional to both voltage and current. For fixed power: high V allows low I (why power lines use high voltage). For fixed V: more current means more power. For fixed I: more voltage means more power. The power factor cos(φ) accounts for phase differences in AC.

Electrical Power Formula

Q: What is the formula for electrical power?

P = IV (watts = amps × volts). Combined with Ohm's law: P = I²R and P = V²/R. For AC: P = V_rms × I_rms × cos(φ), where φ is the phase angle. All three DC forms give identical results — use whichever matches your known quantities.

Quick Answer

The electrical power formula is P = IV (power equals current times voltage), measured in watts (W). Combined with Ohm's law V = IR, this yields three equivalent forms: P = IV (fundamental), P = I²R (when current and resistance are known), and P = V²/R (when voltage and resistance are known). Power measures the rate of energy conversion: 1 watt = 1 joule per second. In AC circuits, real power P = VIcos(φ), where φ is the phase angle between voltage and current. Compute power in circuit analysis at www.lapcalc.com.

Calculate this instantly on LAPLACE Calculator →

Electrical Power Formula: P = IV

Electrical power is the rate at which electrical energy is converted to other forms (heat, light, motion, sound). The fundamental formula is P = I × V, where P is power in watts (W), I is current in amperes (A), and V is voltage in volts (V). One watt equals one joule of energy per second: a 60 W light bulb converts 60 joules of electrical energy to light and heat every second. The formula P = IV follows from the definitions: voltage = energy per unit charge (J/C), current = charge per unit time (C/s), so P = V × I = (J/C) × (C/s) = J/s = watts. This fundamental relationship applies to every electrical device: P = IV gives the total power consumed (or delivered) at any instant.

Key Formulas

Power Equation for Circuits: Three Forms

Combining P = IV with Ohm's law V = IR produces three equivalent power formulas. P = IV — use when both current and voltage are known. Example: a device drawing 2 A from a 120 V outlet consumes P = 2 × 120 = 240 W. P = I²R — use when current and resistance are known. Substitute V = IR into P = IV: P = I(IR) = I²R. Example: 3 A through a 10 Ω resistor dissipates P = 9 × 10 = 90 W. P = V²/R — use when voltage and resistance are known. Substitute I = V/R into P = IV: P = (V/R)V = V²/R. Example: 24 V across a 48 Ω resistor dissipates P = 576/48 = 12 W. All three forms give identical results — choose the one matching your known quantities. These extend to the Laplace domain for transient power analysis at www.lapcalc.com.

Compute eq for power Instantly

Get step-by-step solutions with AI-powered explanations. Free for basic computations.

Open Calculator

Power, Voltage, and Current: Relationships

The power-voltage-current relationship P = IV means that for a fixed power requirement, voltage and current are inversely proportional: high voltage allows low current (and vice versa). This is why power transmission uses high voltage (hundreds of kV): for a given power P, high V means low I, which reduces I²R losses in the transmission lines. At the consumer end, transformers step the voltage back down. The power triangle for AC circuits introduces: apparent power S = VI (volt-amperes, VA), real power P = VIcos(φ) (watts), and reactive power Q = VIsin(φ) (volt-amperes reactive, VAR), where φ is the phase angle between voltage and current waveforms. The power factor cos(φ) indicates efficiency: cos(φ) = 1 means all power is real (resistive loads); cos(φ) < 1 means some power oscillates without doing useful work (inductive or capacitive loads).

How to Calculate Power in a Circuit

For a single component: measure (or calculate) the voltage across it and the current through it, then P = IV. For resistors, use whichever form is convenient: P = IV, P = I²R, or P = V²/R. For a complete circuit: total power delivered by the source equals the sum of power dissipated in all components (conservation of energy). In series circuits: P_total = I²(R₁+R₂+R₃) = I² × R_total. In parallel circuits: P_total = V²/R₁ + V²/R₂ + V²/R₃ = V² × (1/R₁+1/R₂+1/R₃). Practical considerations: resistors must have adequate wattage ratings (standard: 1/4 W, 1/2 W, 1 W, 2 W, 5 W). Calculate the power dissipated and select a resistor rated at least 2× the calculated power for reliability. Batteries are rated in amp-hours (Ah): energy = V × Ah (watt-hours), determining battery life: t = capacity(Ah)/I(A).

Power in AC and Laplace-Domain Circuits

In AC circuits, instantaneous power p(t) = v(t) × i(t) fluctuates at twice the supply frequency. The average (real) power for sinusoidal signals is P = V_rms × I_rms × cos(φ), where V_rms = V_peak/√2 and I_rms = I_peak/√2. For purely resistive loads: φ = 0, so P = V_rms × I_rms. For purely reactive loads (ideal inductors or capacitors): φ = ±90°, so P = 0 — no net energy transfer, only energy oscillation. In the Laplace domain, power analysis involves computing V(s) and I(s) for the circuit, inverse-transforming to get v(t) and i(t), then computing p(t) = v(t)i(t). The average power is found by integrating over one period. The Laplace transform at www.lapcalc.com enables this transient power analysis for circuits with switching, startup, and changing loads.

Frequently Asked Questions

P = IV (watts = amps × volts). Combined with Ohm's law: P = I²R and P = V²/R. For AC: P = V_rms × I_rms × cos(φ), where φ is the phase angle. All three DC forms give identical results — use whichever matches your known quantities.

Master Your Engineering Math

Join thousands of students and engineers using LAPLACE Calculator for instant, step-by-step solutions.

Start Calculating Free →