Question

Why is the equation for AC voltage (E = E_texts sin wt) different from the standard 230V AC voltage supplied to homes?

A) It depends on the material used in the wires.
B) It varies due to the resistance in the circuit.
C) It's the effective voltage (RMS) value.
D) It's a measure of peak voltage.

Answer 1

The equation V = Vo sin wt is for instantaneous voltage in an AC system, varying sinusoidally with time, where Vo is the peak voltage. The standard household voltage, such as 230V, is actually the rms voltage, representing the equivalent DC voltage in terms of power delivery.

Step-by-step explanation:

The equation for alternating current (AC voltage) is V = Vo sin wt, which differs from the standard 230V AC voltage supplied to homes because it represents the instantaneous voltage at any time t, where Vo is the peak voltage and w is the angular frequency.

The standard voltage we refer to, such as 230V in Europe, is actually the rms voltage (root mean square), which is a type of average used to express an AC voltage of a sinusoidally varying waveform. It's important because the rms voltage represents the equivalent DC voltage that would deliver the same power to the load, hence it is a more practical measure for household and common electrical appliances.