Question

a heater is supplied with a dc voltage of 117.0 v and delivers 1.00 kw of heat. what rms voltage must an ac voltage source provide to deliver the same amount of heat?

Answer 1

The rms voltage will be 82.7 v

What is rms voltage?

"RMS" stands for Root Mean Square and is a way of describing the amount of AC voltage or current in terms that are functionally equivalent to DC. For example, 10 Volts AC RMS is the amount of voltage that will produce the same amount of heat dissipation in a given value resistor as a 10 Volts DC power supply.

The root mean square (rms) voltage of a sinusoidal source of emf (Vrms) is used to characterize the source. It is the square root of the square of the time-averaged voltage. The value of Vrms is v₀/√2 or equivalently 0.707 v₀

For the given question:

At the same time interval same heat is produced. Therefore, power in both DC and AC will also be same.

So the rms voltage will be:

= 117.0/√2

= 117.0 × 0.7071

= 82.7 v

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