Question

Two resistors of $100\,\Omega$ each are connected in series with a $9\,\text{V}$ battery. A voltmeter of $400\,\Omega$ resistance is connected to measure the voltage drop across one of the resistors. The voltmeter reading is ___ V.

• A. $2$
• B. $3$
• C. $4$
• D. $4.5$
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Hint:

A voltmeter always alters the circuit because of its finite resistance; use parallel resistance rules carefully.

Answer 1

The Correct Option is C

To solve this problem, let's start by understanding the circuit configuration and calculating the effective resistance and potential difference across the required section. Here are the steps:

1. There are two resistors, each of \(100 \, \Omega\), connected in series. Therefore, the total resistance of the resistors in series is:
2. A \(400 \, \Omega\) voltmeter is connected across one of these \(100 \, \Omega\) resistors to measure the voltage drop. This means the voltmeter and the \(100 \, \Omega\) resistor are in parallel:
3. Now, the resultant parallel resistance \(R_{\text{parallel}} = 80 \, \Omega\) is in series with the other \(100 \, \Omega\) resistor. So, the total circuit resistance is:
4. Using Ohm's Law, the total current \(I\) flowing in the circuit can be found using the formula:
5. Now, calculate the voltage drop across the original \(100 \, \Omega\) resistor using Ohm’s Law again:
6. This \(5 \, \text{V}\) drop occurs across the \(100 \, \Omega\) resistor and the parallel connected voltmeter arrangement. The effective voltage across the voltmeter is:

Therefore, the voltmeter reading is \(4 \, \text{V}\), which is the correct answer.