Question

A battery of emf $1.4 V$ and internal resistance $2 \Omega$ is connected to a $100 \Omega$ resistor through an ammeter. The resistance of the ammeter is $4 / 3 \Omega$. A voltmeter is also connected to find the potential difference across the resistor. The voltmeter reads $1.10 V$. What is the error in reading?

• A. $0.3 V$
• B. $0.43 V$
• C. $0.53 V$
• D. $0.23 V$

Answer 1

Answer: (D)

$E = 1.4 \,V$

Total resistance in the circuit $=\left[2+\frac{4}{3}+\frac{100 R _{ v }}{100+ R _{ v }}\right]$
$I=\frac{E m f}{\text { Total resistance }}$
$\Rightarrow 0.02 A =\frac{1.4 V }{\left[2+\frac{4}{3}+\frac{100 R _{ v }}{100+ R _{ v }}\right] \Omega}$
$\Rightarrow R _{ v }=200 \Omega$
Potential difference across the voltmeter
$=0.02 A \left[\frac{100 \times 200}{100+200}\right]=1.33 V$
Voltmeter reading $=1.10 V$
$\Rightarrow $ Error $=1.33-1.10=0.23 V$