Question

The output voltage of a transducer with an output resistance of $10k\Omega$ is connected to an amplifier. The minimum input resistance of the amplifier so that the error in recording the transducer output does not exceed 2% is

• A. $10k\Omega$
• B. $49k\Omega$
• C. $490k\Omega$
• D. $1.2k\Omega$

Answer 1

The correct option is C $490k\Omega$

When the reading instrument has zero input impedance, it will read full. V volts is being supplied by the source.

When the reading instrument has resistance 'R' then the measured voltage is
$V\times \frac{R}{R+10}$




$\therefore$ error due to the meter resistance R is 2% (given)

$\therefore \frac{V-\frac{R}{R+10}\times V}{V}\times 100=2$

$\frac{100(R+10-R)}{R+10}=2$

1000 = 2(R + 10)

1000 = 2R + 20

$\therefore 2R=1000-20=980$

$\therefore R=\frac{980}{2}=490k\Omega$