Question

A rectifier type PMMC voltmeter has a sensitivity of $20k\Omega /V.$ A reading of 4.5 V is obtained when measuring a voltage source with an internal resistance on it's 5 V scale. When the scale is changed to 10 V full scale, a reading of 6 V is obtained. The value of the voltage and it's internal resistance R are

• A. $10Vand100k\Omega$
• B. $9Vand100k\Omega$
• C. $10Vand200k\Omega$
• D. $9Vand200k\Omega$

Answer 1

The correct option is B $9Vand100k\Omega$


$V_v=V_s\times \frac{R_v}{R_s+R_v}$

For 5 V scale:
$R_v=V.S_v=5\times 20=100k\Omega$

using above written formula,

$4.5=V_s\times \frac{100}{R_s+100}$ ...(i)

For 10 V scale:

$R_v=10\times 20=200k\Omega$

using same formula

$6=V_s\times \frac{200}{R_s+200}$ ...(ii)

on solving equation (i) and (ii)

$weget,R_s=100k\Omega$

$and{V}_s=9V$