Question

Three voltmeters, all having different internal resistances are joined as shown in figure. When some potential difference is applied across A and B, their readings are $V_1$, $V_2$ and $V_3$. 

Choose the correct option.

• A. $V_1 = V_2$
• B. $V_1 \neq V_3 - V_2$
• C. $V_1 + V_2 > V_3$
• D. $V_1 + V_2 = V_3$

Answer 1

The Correct Option is D

To resolve this, analyze the circuit's voltmeter configuration:

1. Three voltmeters, \(V_1\), \(V_2\), and \(V_3\), are connected across points \(A\) and \(B\) as depicted.
2. Voltmeters measure the potential difference between two points.
3. Assuming ideal voltmeters, \(V_1\) and \(V_2\) are in parallel across the same points.
4. \(V_3\) measures the total potential difference across \(A\) and \(B\), encompassing the readings of \(V_1\) and \(V_2\).
5. Consequently, the potential difference measured by \(V_3\) is the sum of those measured by \(V_1\) and \(V_2\).
6. The governing relationship is therefore: \(V_1 + V_2 = V_3\).

Verification of correct and incorrect options:

• \(V_1 = V_2\): Incorrect; readings may differ due to varying internal resistances.
• \(V_1 eq V_3 - V_2\): This statement is true based on our derivation; however, the option requires a strict inequality.
• \(V_1 + V_2>V_3\): Incorrect; \(V_3\) equals the sum of \(V_1\) and \(V_2\).

Therefore, the correct relationship is: \(V_1 + V_2 = V_3\).

Guidance: When analyzing voltmeters in series or parallel, focus on their role in measuring or dividing potential differences across specified points.