P 2.6-3 An ideal voltmeter is modeled as an open circuit. A more realistic model of a voltmeter is a large resistance. Figure P 2.6-3a shows a circuit with a voltmeter that measures the voltage v_m. In Figure P 2.6-3b the voltmeter is replaced by the model of an ideal voltmeter, an open circuit. Ideally, there is no current in the 100-Ω resistor and the voltmeter measures v_mi = 12 V, the ideal value of v_m. In Figure P 2.6-3c the voltmeter is modeled by the resistance R_m. Now the voltage measured by the voltmeter is

As R_m → ∞, the voltmeter becomes an ideal voltmeter and v_m → v_mi = l2 V. When R_m < ∞, the voltmeter is not ideal and v_m < v_mi. The difference between v_m and v_mi is a measurement error caused by the fact that the voltmeter is not ideal.

(a) Express the measurement error that occurs when R_m = 900 Ω as a percent of v_mi.

(b) Determine the minimum value of R_m required to ensure that the measurement error is smaller than 2 percent of v_mi.

Figure P 2.6-3

(a) Express the measurement error that occurs when R_m = 900 Ω as a percent of v_mi.

(b) Determine the minimum value of R_m required to ensure that the measurement error is smaller than 2 percent of v_mi.

To ensure measurement error is less than 2%

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This page last updated on December 29, 2018