Question

A battery of emf $1.4V$ 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 $1.10V$. What is the error in reading?

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

Answer 1

Answer: (D)

$E=1.4V$

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