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VITEEE 2009 Paper

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Question : 28 of 120

Marks: +1, -0

In the adjacent shown circuit, a voltmeter of internal resistance R, when connected across B and C reads

\frac{100}{3}

V. Neglecting the internal resistance of the battery, the value of R is

100 kΩ
75 kΩ
50 kΩ
25 kΩ

Solution:

Internal resistance of voltmeter = R.

Effective resistance across B and C

\frac{1}{R'} = \frac{1}{R} + \frac{1}{50} = \frac{50+R}{50R}

or

R' = \frac{50R}{50+R}

According to Ohm's law,

V' = I R'

or

\frac{100}{3} = I \cdot \frac{50R}{50+R}

or

\frac{100}{3} \cdot \frac{50+R}{50R} = I

...(i)

Now, total resistance of circuit

R^{n} = 50 + \frac{50R}{50+R}

or

R^{n} = \frac{2500+100R}{50+R}

Now,

V^{n} = I R^{n}

⇒

100 = \frac{100}{3} \cdot \frac{50+R}{50R} \cdot \frac{2500+100R}{50+R}

⇒150R = 2500 + 100R or R = 50kΩ

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