Ncert Exercises & Solutions

When a voltage measuring device is connected to AC mains, the meter shows the steady input voltage of

220 V

$220~\text{V}$ . This means:

1.	input voltage cannot be AC voltage, but a DC voltage
2.	maximum input voltage is $220~\text{V}$
3.	the meter reads not $v$ but $<v^2>$ and is calibrated to read $\sqrt{<v^2>}$
4.	the pointer of the meter is stuck by some mechanical defect

Hint: The voltmeter is calibrated to read the root mean square value.

Explanation: In AC voltage, the steady input voltage is the RMS value of the voltage. The voltmeter connected to the AC mains measures the mean value

(< v^{2} >)

$(<v^2>)$ and is calibrated to display the RMS value. It does this by multiplying the measured value

< v^{2} >

$< v^2>$ by the form factor to obtain the RMS voltage. Therefore, the meter reads not

v

$v$ but

< v^{2} >

$<v^2>$ and is calibrated to read

\sqrt{< v^{2} >} .

$\sqrt{<v^2>}.$
Hence, option (3) is the correct answer.

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