question_answer

A voltmeter having a resistance of 998 ohms is connected to a cell of e.m.f. 2 volt and internal resistance 2 ohm. The error in the measurement of e.m.f. will be   [MP PMT 1994]

A)                    \[4\times {{10}^{-1}}\,volt\]

B)                                      \[2\times {{10}^{-3}}volt\]

C)                    \[4\times {{10}^{-3}}volt\]

D)            \[2\times {{10}^{-1}}volt\]

Correct Answer: C

Solution :

             Error in measurement = Actual value ? Measured value                    Actual value = 2V                    \[i=\frac{2}{998+2}=\frac{1}{500}A\]                    Since \[E=V+ir\] Þ \[V=E-ir=2-\frac{1}{500}\times 2=\frac{998}{500}V\]                     \ Measured value \[=\frac{998}{500}V\]            Þ  Error\[=2-\frac{998}{500}=4\times {{10}^{-3}}volt\]