This question tests the fundamental definition of the RMS (Root Mean Square) value of an alternating quantity. The RMS value of an AC voltage or current is defined precisely as that value of a steady DC voltage or current which, when applied to the same resistor over the same time, dissipates exactly the same amount of heat (average power). For this reason RMS is also called the effective or heating value.

The physical basis is that the instantaneous power in a resistor is p = v²/R. Since power depends on the square of the voltage, the correct "equivalent" measure is obtained by squaring the waveform, taking its mean over a cycle, and then taking the square root — hence "root-mean-square":

V_RMS = √( mean of v²(t) )

Here the problem states directly that the AC supply produces the same heating effect as a 20 V DC supply across the same resistor. By definition, the RMS value of that AC voltage must therefore equal the DC voltage giving identical heating, so V_RMS = 20 V. This is the correct choice.

Why the others are wrong:

• The value 28.28 V (≈ 20√2) is the peak voltage that a sinusoidal AC waveform would need to have an RMS of 20 V, since V_peak = V_RMS × √2. It answers a different question (peak, not RMS), and it also assumes a sine wave, which is not required by the definition of RMS.
• The value 14.14 V (≈ 20/√2) reverses that relationship and would be the RMS of a sine wave whose peak is 20 V — again not what is asked.
• 10 V corresponds to no meaningful relationship here; halving the voltage would quarter the heating, so it cannot give the same heating effect as 20 V DC.