Question

# A $110V$ D.C. heater is used on an A.C. source, such that the heat produced is the same as it produces when connected to $110V$ D.C in same time-intervals. What will be the R.M.S. value of the alternating voltage?\begin{align} & A.110V \\ & B.220V \\ & C.330V \\ & D.440V \\ \end{align}

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Hint: Alternating current abbreviated as AC is defined as an electric current that is reversing its direction periodically, which is in contrast to direct current abbreviated as DC which is only flowing in a single direction which cannot vary periodically.

First of all let us take a look at what actually alternating current and the direct current means. Direct current or DC is the flow of electric charge in only one constant direction. It is having a steady state of a constant-voltage circuit. Alternating current or AC is defined as the flow of electric charge that periodically changes its direction.
Here in this question, for the same time interval, same heat is being produced,
Therefore the power will be the same in both alternating current and direct current cases.
Therefore the equation can be written as,
$\dfrac{{{V}^{2}}_{DC}}{R}=\dfrac{{{V}^{2}}_{rms}}{R}=P$
In which $R$ is the resistance of the wire, ${{V}_{DC}}$ is the potential of direct current and ${{V}_{rms}}$ is the potential of alternating current.
Now let us substitute the value in this, as both the denominators are the same we can cancel it.
Therefore the equation becomes,
${{V}_{rms}}={{V}_{DC}}$
Hence,
${{V}_{rms}}=110V$

So, the correct answer is “Option A”.

Note: The major advantage that AC electricity has over DC electricity is that AC voltages are readily transformed to lower or higher voltage levels, while it is hard to do that with direct current voltages. This is due to the high voltages from the power station which can be easily decreased to a safer voltage for its use in the household.