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NEET PHYSICSMOVING CHARGES AND MAGNETISMMedium

Question

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)

A

Exactly 10 \Omega

B

Less than 10 \Omega

C

More than 10 \Omega

D

We cannot definitely say

Step-by-Step Solution

  1. Measurement Setup: In the standard voltmeter-ammeter method to measure an unknown resistance RR, the voltmeter is connected in parallel with the resistor to measure the potential difference (VV), and the ammeter is connected in series to measure the current (II).
  2. Finite Resistance: A real voltmeter has a finite (though large) resistance RVR_V . Therefore, when connected in parallel with RR, it draws a small amount of current (IVI_V) to produce the deflection.
  3. 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 Imeasured=IR+IVI_{measured} = I_R + I_V, where IRI_R is the true current through the resistor.
  4. Resistance Calculation: The apparent or measured resistance is calculated using Ohm's law: Rmeasured=VImeasured=202=10 ΩR_{measured} = \frac{V}{I_{measured}} = \frac{20}{2} = 10\ \Omega.
  5. Comparison: Since the measured current ImeasuredI_{measured} (IR+IVI_R + I_V) is greater than the true current IRI_R, the denominator in the resistance formula is larger than it should be for the true resistance. Rtrue=VIRR_{true} = \frac{V}{I_R}. Since Imeasured>IRI_{measured} > I_R, it follows that Rmeasured<RtrueR_{measured} < R_{true}. Therefore, 10<Rtrue10 < R_{true}. The true resistance is greater than 10 Ω10\ \Omega.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from MOVING CHARGES AND MAGNETISM. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSMOVING CHARGES AND MAGNETISMammetervoltmeterresistanceassumingfinite

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