A rectifier type AC voltmeter consists of a series resistance Rs an ideal full-wave birdge rectifier and a PMMC instrument as shown in the figure- The internal resistance of the instrument is 100 - and a full scale deflection is produced by a DC current of 1 mA- The value of Rs- required to obtain full scale deflection with an AC voltage of 100 Vrmsapplied of the input terminals is

I_FS= nbsp; Current required to produce full scale deflection DC sensitivity is, S_dc=1I_FS =11 mA=10^3 Ω/V For full wave rectifier AC sensitivity S_ ...

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Standard XII

Physics

Resistance of P-N Junction

A rectifier t...

Question

A rectifier type AC voltmeter consists of a series resistance $R_{s}$ an ideal full-wave birdge rectifier and a PMMC instrument as shown in the figure. The internal resistance of the instrument is $100 Ω$ and a full scale deflection is produced by a DC current of 1 mA. The value of $R_{s}$ . required to obtain full scale deflection with an AC voltage of 100 V(rms)applied of the input terminals is

63.56 Ω

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69.93 Ω

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89.93 Ω

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141.3 Ω

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Solution

The correct option is C $89.93 Ω$
$I_{F S} = C u r r e n t r e q u i r e d t o p r o d u c e f u l l s c a l e d e f l e c t i o n$

DC sensitivity is,
$S_{d c} = \frac{1}{I_{F S}}$
$= \frac{1}{1 m A} = 10^{3} Ω / V$

For full wave rectifier AC sensitivity
$S_{A C} = 0.9 S_{D C} = 900 Ω / V$

Resistance of multiplier
$R_{s} = S_{A C} V - R_{m} - 2 R_{d}$

Since, diodes are ideal,
$R_{d} = 0$

then,
$R_{s} = 900 \times 100 - 100$
$= 89.9 k Ω$

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The correct option is C 89.93ΩIFS=Current required to produce full scale deflection DC sensitivity is, Sdc=1IFS =11mA=103Ω/V For full wave rectifier AC sensitivity SAC=0.9SDC=900Ω/V Resistance of multiplier Rs=SACV−Rm−2Rd Since, diodes are ideal, Rd=0 then, Rs=900×100−100 =89.9kΩ