Two resistances of 400 Ωand 800 Ωconnected in series with a 6 volt battery of negligible interna

step 1 In this question we will learn about some basic concept of the units and measurement. The questi

Two resistances of 400 Ωand 800 Ωconnected in series with a...

Two resistances of $400 \Omega$ and $800 \Omega$ connected in series with a 6 volt battery of negligible internal resistance. A voltmeter of resistance $10,000 \Omega$ is used to measure the potential difference across $400 \Omega$. The error in the measurement of potential difference in volts approximately is (A) $0.01$ (B) $0.02$ (C) $0.04$ (D) $0.05$

Key Concepts

Voltage Divider

This concept involves dividing the total voltage of a circuit among series-connected resistors proportionally to their resistances. It is fundamental in circuits to determine the potential drop across an individual resistor and is used here to find the expected voltage across the 400 ? resistor in the absence of measurement interference.

Loading Effect

The loading effect describes how the act of measurement can alter the circuit being measured. In circuits, measuring devices like voltmeters have finite resistance that, when connected, can change the effective resistance and thus the voltage distribution. This concept is crucial when considering the measurement error introduced by a voltmeter with non-infinite resistance.

Parallel Resistance

When a voltmeter is connected across a resistor, it forms a parallel combination with that resistor. The effective resistance of this parallel combination is less than the resistance of the individual resistor, thereby modifying the voltage drop across it. This principle is important for calculating the altered measurements in the given problem.

Error Analysis in Measurements

This concept involves comparing the theoretical value of a circuit parameter (obtained without measurement interference) with the actual value measured when non-ideal instruments are used. In this context, the error is determined by the difference in potential across a resistor with and without the influence of the voltmeter's resistance.

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