Question

If the reading of AC mains voltage by a voltmeter is 200V, then the rms value of this voltage is_______

Answer 1

Given:

Reading of AC main voltage by a voltmeter is 200V.

To find:

Root Mean Square (RMS) value of the voltage.

Calculation:

• In Alternating Current circuits , the voltage periodically oscillates between the peak voltage values following are sinusoidal relationship with time.

• However , whenever a voltmeter is attached to the alternating circuit it always reads the root mean square value (RMS) of the voltage.

• This means that the RMS value of the voltage is equal to 200 volts.

RMS value = 200 V ;

$\sf{peak \: voltage = \sqrt{2} \times (rms \: voltage)}$

$= > \sf{peak \: voltage = \sqrt{2} \times 200}$

$= > \sf{peak \: voltage = 200 \sqrt{2} \: volt}$

So , final answer is :

$\boxed{ \sf{RMS \: voltage = 200 \: volt}}$

Answer 2

Given:

The reading of AC mains voltage by a voltmeter is 200V

To find:

If the reading of AC mains voltage by a voltmeter is 200V, then the rms value of this voltage is

Solution:

From given, we have,

The reading of AC mains voltage by a voltmeter is 200 V

⇒ Vp = 200 V

The formula that relates the peak voltage with the rms voltage is given by,

Vp = √2 Vrms

Therefore, upon substituting the given values in the above equation, we get,

200 = √2 ×  Vrms

Vrms = 200/√2

Vrms = 200/1.414

∴ Vrms = 141.44 V.

Therefore, the  rms value of the reading of AC mains voltage by a voltmeter is 141.44 V