Q176 / 180 · COMEDK 2024 (Evening Shift) · Physics
A voltmeter of resistance $1000 \Omega .0 .5 \mathrm{~V} /$ div is to be converted into a voltmeter to make it to read $=1 \mathrm{~V} / \mathrm{div}$. The value of high resistance to be connected in series with it is
- A$4000 \Omega$
- Correct answerB$1000 \Omega$
- C$6000 \Omega$
- D$5000 \Omega$
Solution
The sensitivity of the voltmeter is given as $S_1 = 0.5 \text{ V/div}$. The resistance of the voltmeter is $R_V = 1000 \Omega$.
The full scale deflection current $I_g$ is given by $I_g = \dfrac{V_{div}}{R_V} = \dfrac{0.5}{1000} = 5 \times 10^{-4} \text{ A}$.
The new sensitivity required is $S_2 = 1 \text{ V/div}$. Let the new total resistance be $R_{total} = R_V + R_s$, where $R_s$ is the series resistance to be added.
For the new sensitivity, $I_g = \dfrac{S_2}{R_V + R_s}$.
Substituting the values: $5 \times 10^{-4} = \dfrac{1}{1000 + R_s}$.
$1000 + R_s = \dfrac{1}{5 \times 10^{-4}} = \dfrac{10000}{5} = 2000$.
$R_s = 2000 - 1000 = 1000 \Omega$.
Answer: $1000 \Omega$
The full scale deflection current $I_g$ is given by $I_g = \dfrac{V_{div}}{R_V} = \dfrac{0.5}{1000} = 5 \times 10^{-4} \text{ A}$.
The new sensitivity required is $S_2 = 1 \text{ V/div}$. Let the new total resistance be $R_{total} = R_V + R_s$, where $R_s$ is the series resistance to be added.
For the new sensitivity, $I_g = \dfrac{S_2}{R_V + R_s}$.
Substituting the values: $5 \times 10^{-4} = \dfrac{1}{1000 + R_s}$.
$1000 + R_s = \dfrac{1}{5 \times 10^{-4}} = \dfrac{10000}{5} = 2000$.
$R_s = 2000 - 1000 = 1000 \Omega$.
Answer: $1000 \Omega$
Hence, the correct answer is option: 'B'.