Solved: PHYSICS Question for NEET

NEET PHYSICSMedium

If an ammeter A reads 2 A and the voltmeter V reads 20 V, what is the value of resistance R? (Assuming finite resistances of ammeter and voltmeter)

Exactly 10 \Omega

Less than 10 \Omega

More than 10 \Omega

We cannot definitely say

Measurement Setup: In the standard voltmeter-ammeter method to measure an unknown resistance $R$ , the voltmeter is connected in parallel with the resistor to measure the potential difference ( $V$ ), and the ammeter is connected in series to measure the current ( $I$ ).
Finite Resistance: A real voltmeter has a finite (though large) resistance $R_V$ . Therefore, when connected in parallel with $R$ , it draws a small amount of current ( $I_V$ ) to produce the deflection.
Current Analysis: The ammeter, being in the main line, measures the total current supplied to the parallel combination of the resistor and the voltmeter. Thus, the ammeter reading is $I_{measured} = I_R + I_V$ , where $I_R$ is the true current through the resistor.
Resistance Calculation: The apparent or measured resistance is calculated using Ohm's law: $R_{measured} = \frac{V}{I_{measured}} = \frac{20}{2} = 10\ \Omega$ .
Comparison: Since the measured current $I_{measured}$ ( $I_R + I_V$ ) is greater than the true current $I_R$ , the denominator in the resistance formula is larger than it should be for the true resistance. $R_{true} = \frac{V}{I_R}$ . Since $I_{measured} > I_R$ , it follows that $R_{measured} < R_{true}$ . Therefore, $10 < R_{true}$ . The true resistance is greater than $10\ \Omega$ .

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