JEE Physics 2023 Question with Solution

Given: Assertion $A$ compares voltmeters of resistance $1000 \, \Omega$ and $4000 \, \Omega$ for measuring potential difference across a resistor of $600 \, \Omega$. Reason $R$ states that a voltmeter with higher resistance draws smaller current.

Find: Which option correctly evaluates Assertion $A$ and Reason $R$.

A practical voltmeter should have very high resistance so that it draws minimum current from the circuit and does not disturb the potential difference being measured.

For a resistor of $600 \, \Omega$, the voltmeter of resistance $4000 \, \Omega$ is preferred over the voltmeter of resistance $1000 \, \Omega$ because the higher-resistance voltmeter is closer to an ideal voltmeter.

Therefore, Assertion $A$ is incorrect.

Now consider Reason $R$. Using Ohm's law,

$$I = \frac{V}{R}$$

for a given potential difference, the current drawn is smaller when the resistance is larger.

So, a voltmeter with higher resistance will draw smaller current than a voltmeter with lower resistance. Therefore, Reason $R$ is correct.

Hence, Assertion $A$ is false but Reason $R$ is true. The correct option is C.

Note: The option text labeled C on the source solution corresponds to 'A is not correct but R is correct' in the given options, so the solution's has a labeling mismatch. Based on the provided options, the matching statement is option A, but the solution explicitly concludes option C.

Given: A voltmeter is used to measure potential difference across a resistance of $600 \, \Omega$.

Find: Whether Assertion $A$ and Reason $R$ are true.

An ideal voltmeter has infinite resistance. In practice, the larger the resistance of the voltmeter, the smaller the current it draws when connected in parallel.

If the voltmeter resistance is not sufficiently large, it changes the effective parallel combination and affects the measured voltage more significantly. Therefore, among $1000 \, \Omega$ and $4000 \, \Omega$, the voltmeter of $4000 \, \Omega$ is better.

Thus, Assertion $A$ is false.

Reason $R$ is true because for the same applied voltage,

$$I \propto \frac{1}{R}$$

so higher resistance means lower current.

Therefore, the correct logical conclusion is: Assertion $A$ is not correct but Reason $R$ is correct.