AC Voltage at Home is 230V but its Equation is v = Vm Sin θ. Explain?

Domestic AC Voltage at Home is 230V but its Equation is v = V_m Sin θ. Explain the Difference?

Our homes are supplied with sinusoidal voltage whose equation should be (v = V_m Sin θ). But we always say that AC voltage at home is 230V. How do you explain this difference?

The domestic single phase AC supply is 230V, 50Hz (in EU) or 110V 60Hz in US. It is the RMS or effective value. It means that alternating voltage available has the same heating effect as 230V DC. The equation of this alternating voltage:

v = V_m Sin θ

v = V_m Sin ωt ….. (θ = ωt)

v = 230V_RMS x √2 Sin 2π x 50 t ….. [Putting V_m = √2 V_RMS and ω = 2π]

v = 230V_RMS x √2 Sin 314 t Volts

In short, the figure of 110V or 230V is not the exact value of sinusoidal voltage at our homes supplied by the power house. But it is the exact value of RMS voltage i.e. we get the amount of AC voltage having the same effect of 110V DC or 230VDC respectively.

Keep in mind that the 230V AC in domestic supply has the peak value of 325V_P (Peak Voltage) or 650V_P-P (Peak to Peak Voltage) and 207V_AVG (Average Voltage).

Same is the case for 110V AC which peak voltage, peak to peak voltage and average voltage are 155V_P, 310V_P-P, 99V_AVG respectively by using the RMS value calculator and peak voltage calculator.

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