A voltmeter of resistance \( 150\,\Omega \) is connected across A and B in the given circuit. The reading of voltmeter will be :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 15 V
A real voltmeter draws current, so it acts as a resistor in parallel with the part of the circuit it is connected across. The two resistors are \( 100\,\Omega \) each (resistances in ohms), and the cell is taken as ideal.
The voltmeter in parallel with the \( 100\,\Omega \) resistor between A and B:
\( \displaystyle R_{AB} = \frac{100 \times 150}{100 + 150} = 60\,\Omega \)
This is in series with the \( 100\,\Omega \) resistor between B and C:
\( \displaystyle R_{\mathrm{total}} = 60 + 100 = 160\,\Omega \)
\( \displaystyle I = \frac{40\,\mathrm{V}}{160\,\Omega} = 0.25\,\mathrm{A} \)
The voltmeter reads the potential difference across A and B:
\( \displaystyle V_{AB} = I R_{AB} = 0.25 \times 60 = 15\,\mathrm{V} \)