DC power calculation .

Electric Power in DC and AC

1. Power in Direct Current (DC)

In direct current, the voltage (U) and the current (I) remain constant over time.

Formula: P = U × I

P = power in watts (W)
U = voltage in volts (V)
I = current in amperes (A)

Power is always real. There is no phase shift.

2. Power in Alternating Current (AC)

In alternating current, voltage and current vary over time, usually in a sinusoidal form:

u(t) = Umax × sin(ωt)
i(t) = Imax × sin(ωt + φ)

φ (phi) is the phase angle between voltage and current.

Here are the three types of power:

Active Power (P) = Ueff × Ieff × cos(φ)
Reactive Power (Q) = Ueff × Ieff × sin(φ)
Apparent Power (S) = Ueff × Ieff

cos(φ) is the power factor and reflects the circuit's efficiency.

Numerical Example

Let's consider an AC motor:

U = 230 V
I = 10 A
φ = 30°

P = 230 × 10 × cos(30°) ≈ 1991 W
Q = 230 × 10 × sin(30°) ≈ 1150 VAR
S = 230 × 10 = 2300 VA

Power Triangle

apparent power, active power, and reactive power. These are all interconnected through the power triangle.

Apparent Power

Apparent power is the trigonometric sum of active and reactive power. It is also the power subscribed to in an electricity contract (expressed in kVA).

Formula: S = U × I

S = apparent power (VA)
U = voltage (V)
I = current (A)

Apparent power is the hypotenuse of the power triangle. Using Pythagoras' theorem, we can also calculate it as:

S = √(P² + Q²)
S = apparent power (VA)
P = active power (W)
Q = reactive power (VAR)

Active Power

Active power is the power that produces real work — it can be considered the "useful" part. It's often confused with apparent power. In residential use, it represents the majority of energy consumption.

Formula: P = U × I × cos(φ)

P = active power (W)
U = voltage (V)
I = current (A)
φ = phase angle (degrees)

Reactive Power

Reactive power is less known and more complex. It doesn't produce usable work, but it's essential in many systems — especially those with inductive components such as motors, refrigeration units, or some electronics. Purely resistive devices (like basic heaters) do not require reactive power.

Reactive power can be compensated with capacitor banks, which can supply the required reactive energy.

Formula: Q = U × I × sin(φ)

Q = reactive power (VAR)
U = voltage (V)
I = current (A)
φ = phase angle (degrees)

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Components,Module & IC.

Resistor.

Transistor.

Capacitor.

Diode.

thyristor.

inductor.

optocoupler.

regulator.

hall effect sensor.

diac.

transformer.

ceramic resonator.

relay.

fuse.

micro electret.

quartz.

NE555.

TL494.

TDA2822.

LM386.

TDA3886.

serie 74HCXX.

OP amp.

Arduino.