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 solve this problem, let's understand the configuration of the voltmeters in the circuit provided: 

1. We have three voltmeters, \(V_1\), \(V_2\), and \(V_3\), connected across points \(A\) and \(B\) in the given figure.
2. The key point to understand is how voltmeters work: they measure the potential difference between two points.
3. In the circuit shown, \(V_1\) and \(V_2\) are in parallel and essentially across the same two points (assuming ideal voltmeters for simplicity).
4. \(V_3\) measures the total potential difference across \(A\) and \(B\) which includes both \(V_1\) and \(V_2\).
5. This means the overall potential difference that \(V_3\) measures is the sum of what \(V_1\) and \(V_2\) are measuring.
6. Thus, the correct relationship is: \(V_1 + V_2 = V_3\).

Now, let's verify why this option is correct and others are not:

• \(V_1 = V_2\): This is incorrect since they can have different readings due to different internal resistances.
• \(V_1 \neq V_3 - V_2\): This statement is true due to our conclusion, but the option requires a strict inequality assertion.
• \(V_1 + V_2 > V_3\): This cannot be true, as per our principle, \(V_3\) is the sum of \(V_1 + V_2\).

Thus, the correct answer is: \(V_1 + V_2 = V_3\).

Tip: When dealing with voltmeters in series or parallel, always consider how they split or measure potential difference across points.

Answer 2

Applying Kirchhoff’s Voltage Law (KVL) across the loop: \(V_1 + V_2 - V_3 = 0 \implies V_1 + V_2 = V_3.\)

The Correct answer is: $V_1 + V_2 = V_3$