A d.c. voltmeter has a sensitivity of 1000 O/volt. When it measures half full scale in 100V range, the current through the voltmeter will be:
a. 100mA
b. 0.5mA
c. 50mA
d. 1mA
The correct answer and explanation is :
The correct answer is b. 0.5mA.
Explanation:
The problem involves a DC voltmeter with a sensitivity of 1000 ohms per volt. Sensitivity refers to the internal resistance of the voltmeter for each volt of full-scale reading. In other words, for every volt that the voltmeter measures, it behaves like it has a resistance of 1000 ohms.
Step 1: Determine the resistance of the voltmeter.
Since the voltmeter has a sensitivity of 1000 ohms per volt, for any voltage reading, the resistance of the voltmeter is calculated as:
[
R_{vm} = 1000 \, \Omega/\text{V} \times \text{Voltage measured in volts}
]
Step 2: Understand the measurement situation.
The voltmeter is set to measure a 100V range, and it measures half of the full scale. Therefore, the voltage being measured is:
[
V_{measured} = 100V \times \frac{1}{2} = 50V
]
Step 3: Calculate the internal resistance of the voltmeter.
From the sensitivity specification of 1000 ohms per volt, the internal resistance of the voltmeter when measuring 50V would be:
[
R_{vm} = 1000 \, \Omega/\text{V} \times 50V = 50,000 \, \Omega
]
Step 4: Calculate the current through the voltmeter.
Next, we apply Ohm’s law to calculate the current through the voltmeter. Assuming the voltmeter is connected in parallel with the voltage source, the current through the voltmeter is given by:
[
I = \frac{V}{R_{vm}} = \frac{50V}{50,000 \, \Omega} = 0.001A = 1mA
]
So, the current through the voltmeter when it reads half of its full-scale value (50V on a 100V range) is 1mA. This matches option d. 1mA.
Conclusion:
Despite the confusion in the wording of the question, the correct analysis leads to the answer that the current through the voltmeter is 1mA when it measures 50V on the 100V range. This corresponds to answer d. 1mA.