First slide

Sources of emf and Kirchhoff's laws

Question

The actual value of resistance ‘R’ shown in the figure is $50 Ω$ . This is measured in an experiment as shown using the standard formula $R = \frac{V}{I}$ where V and I are the readings of Voltmeter and Ammeter respectively . If the measured value of R is 5% less, then the internal resistance of the voltmeter is,

Moderate

Solution

$T h e a c t u a l v a l u e i s R = 50 Ω b u t m e a s u r e d v a l u e i s 0.95 R (∵ 5 % l e s s t h a n o r i g i n a l i . e ., R - 5 % R = R - \frac{5 R}{100} = 0.95 R) R a n d R_{V} (∵ R_{V} = r e s i s \tan c e o f v o l t m e t e r) a r e i n p a r a l l e l . R_{e q} = \frac{{RR}_{V}}{{R+R}_{V}} \Rightarrow 0.95 R = \frac{{RR}_{V}}{{R+R}_{V}} \Rightarrow R_{v} = 19 R \Rightarrow R_{v} = 19 \times 50 = 950 Ω$

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