A voltmeter with 200-k Ωresistance is used to measure the...

A voltmeter with $200-\mathrm{k} \Omega$ resistance is used to measure the voltage across the $10-\mathrm{k} \Omega$ resistor in Fig. $25.27 .$ By what percentage is the measurement in error because of the finite meter resistance? (FIGURE CANT COPY)

Key Concepts

Parallel Resistance Combination

When a voltmeter is connected across a resistor, the effective resistance seen by the circuit is the parallel combination of the resistor and the voltmeter’s internal resistance. This new combined resistance is lower than the original resistor value, leading to a modified voltage-divider network within the circuit and an inaccurate voltage reading.

Measurement Error

Measurement error here quantifies the discrepancy between the true value of the voltage across the resistor and the value measured by the voltmeter due to its finite internal resistance. The percentage error can be calculated by comparing the voltage reduction caused by the parallel resistance effect to the actual voltage that would exist if the meter were ideal.

Voltmeter Input Resistance

This concept refers to the internal resistance of a voltmeter, which ideally should be infinite so that it draws no current from the circuit. However, in practical applications, the internal resistance is finite, and this can affect the circuit by drawing a small amount of current when connected, thereby altering the voltage distribution.

Loading Effect

The loading effect describes the influence a measuring device has on a circuit when it is connected. In the context of voltage measurement, the finite resistance of the voltmeter forms a parallel combination with the circuit element under test, which can result in a voltage drop that differs from the true voltage present in the circuit without the meter attached.

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