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.
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.
- $V_1 = V_2$
- $V_1 \neq V_3 - V_2$
- $V_1 + V_2 > V_3$
- $V_1 + V_2 = V_3$
The Correct Option is D
Approach Solution - 1
To solve this problem, let's understand the configuration of the voltmeters in the circuit provided:
- We have three voltmeters, \(V_1\), \(V_2\), and \(V_3\), connected across points \(A\) and \(B\) in the given figure.
- The key point to understand is how voltmeters work: they measure the potential difference between two points.
- In the circuit shown, \(V_1\) and \(V_2\) are in parallel and essentially across the same two points (assuming ideal voltmeters for simplicity).
- \(V_3\) measures the total potential difference across \(A\) and \(B\) which includes both \(V_1\) and \(V_2\).
- This means the overall potential difference that \(V_3\) measures is the sum of what \(V_1\) and \(V_2\) are measuring.
- 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.
Approach Solution -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: $V_1 + V_2 = V_3$
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