Question

For the network shown in the figure, the voltage across terminal AB is measured by a voltmeter. The sensitivity of voltmeter is $2k\Omega /volt$. Which of the following statement is true?

• A. $\text{Voltmeter has 27.27\% error}$
• B. $\text{Resistance of voltmeter =}100k\Omega$
• C. $\text{Voltage across CD = 33.33 V}$
• D. $\text{Equivalent resistance across CD = 36.36 k}\Omega$

Answer 1

Answer: (A), (B)

$\text{Resistance of voltmeter =}100k\Omega$

For voltmeter;
Voltage across $50k\Omega$ resistor

$=\frac{200}{150+150}\times 50=50V$

Resistance of voltmeter $=S_{\nu }\times V=2\times 50=100k\Omega$

Equivalent resistance across CD

$=\frac{50\times 100}{50+100}=\frac{100}{3}k\Omega$

Voltage across CD considering meter resistance,

$V_{CD}=\frac{100/3}{\frac{100}{3}+150}\times 200=\frac{100\times 200}{550}=36.36V$

$Error=\frac{(50-36.36)}{50}\times 100\%=27.27\%$