Calculation Example: Alternating Current

Calculation Example

1. Problem Statement

A household electrical outlet provides an AC voltage specified as $220 \text{ V}_{rms}$ at $50 \text{ Hz}$ . Write the time-domain equation for this voltage, assuming a phase angle of $0^\circ$ .

2. Given Information

RMS Voltage (Vrms)

Frequency (f)

Phase Angle (Phase)

3. Formulas and Calculation

Step 1: Calculate peak amplitude ( $V_m$ )

Error: Formula electrical-ac-fundamentals not found in the Formula Registry.

Step 2: Calculate angular frequency ( $\omega$ )

Error: Formula electrical-ac-fundamentals not found in the Formula Registry.

Step 3: Construct the time-domain equation The time-domain equation for this voltage is: $v(t) = 311.1 \sin(314.16 t) \text{ V}$ (Result: )

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Calculation Example: Alternating Current