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

Step 1: Finding equivalent resistance across measured branch.
The voltmeter is connected in parallel with one $100\,\Omega$ resistor.
\[ R_{\text{parallel}} = \dfrac{100 \times 400}{100 + 400} = 80\,\Omega \] Step 2: Finding total circuit resistance.
\[ R_{\text{total}} = 100 + 80 = 180\,\Omega \] Step 3: Calculating current from the battery.
\[ I = \dfrac{9}{180} = 0.05\,\text{A} \] Step 4: Finding voltmeter reading.
\[ V = I \times 80 = 0.05 \times 80 = 4\,\text{V} \] Step 5: Final conclusion.
The voltmeter reads $4\,\text{V}$.