Electric power calculation formula - Solutions - Huaqiang Electronic Network

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(1) In a series circuit, the current remains constant throughout: I₁ = I₂ = I. The total voltage is the sum of the voltages across each component: U = U₁ + U₂. The total resistance is the sum of individual resistances: R = R₁ + R₂. The voltage ratio across components equals their resistance ratio: U₁:U₂ = R₁:R₂. Total electric work is the sum of each component's work: W = W₁ + W₂. The work ratio also follows the resistance or voltage ratio: W₁:W₂ = R₁:R₂ = U₁:U₂. Similarly, power ratios are proportional to resistance or voltage: P₁:P₂ = R₁:R₂ = U₁:U₂. Total power is the sum of individual powers: P = P₁ + P₂.

(2) In a parallel circuit, the total current is the sum of the branch currents: I = I₁ + I₂. Voltage remains the same across all branches: U₁ = U₂ = U. Total resistance is calculated using the formula: R = (R₁ × R₂) / (R₁ + R₂). Electric work is additive: W = W₁ + W₂. Current ratio is inversely proportional to resistance: I₁:I₂ = R₂:R₁. Work and power ratios follow the same pattern: W₁:W₂ = I₁:I₂ = R₂:R₁, and P₁:P₂ = R₂:R₁ = I₁:I₂. Total power is again the sum of individual powers: P = P₁ + P₂.

(3) For the same electrical device, the rated power (Pe) compared to actual power (Ps) is determined by the square of the ratio of rated voltage (Ue) to actual voltage (Us): Pe/Ps = (Ue/Us)². This relationship is crucial when evaluating performance under different voltage conditions.

2. Circuit Formulas

(1) Resistance (R): - R = ρ × (L/S), where ρ is resistivity, L is length, and S is cross-sectional area. - R = U/I, where U is voltage and I is current. - R = U²/P, where U is voltage and P is power.

(2) Electric Work (W): - W = UIT (general formula) – current × voltage × time. - W = PT (power × time). - W = QT (charge × voltage). - W = I²RT (for pure resistance circuits). - W = U²T/R (also for pure resistance circuits).

(3) Electric Power (P): - P = UI (voltage × current). - P = I²R (for pure resistance circuits). - P = U²/R (for pure resistance circuits). - P = W/T (work divided by time).

(4) Electric Heating (Q): - Q = I²Rt (general formula for heat generated). - Q = UIT = W (for pure resistance circuits).