Discussion
It is desired to measure the voltage across the 50 KΩ resistor for the given circuit. A voltmeter with a sensitivity of 20,000 Ohms/V is used on its 50 V range. What will be the reading indicated by the voltmeter?
Answer: A
A voltmeter of sensitivity 20,000 ohms per volt on its 50 V range has a resistance of 20000 x 50 = 1 mega-ohm. Connected across the 50 kilo-ohm resistor it forms a parallel pair of about 47.6 kilo-ohm. This is in series with the 100 kilo-ohm resistor, so the voltage it reads is
\[ V = 150 \times \frac{47.6}{100 + 47.6} \]
\[ V \approx 48.4\ \mathrm{V} \]
The key gives 48.36 V, option (A). The true voltage without the meter would be 50 V, and the meter loads the circuit and reads less, so 50 V, 53 V and 45.33 V are not what it indicates.
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