An ideal voltmeter is modeled as an open circuit. A more realistic model of a voltmeter is a large resistance. Figure (a) shows a circuit with a voltmeter that measures the voltage vm. In figure (b) 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 vmi = 12 V, the ideal value of vm. In figure (c) below the voltmeter is modeled by the resistance Rm.

(a) Derive the voltage measured by the voltmeter (voltage across the voltmeter ) Hint : Rm → ∞, the voltmeter becomes an ideal voltmeter and vm → vmi = l2 V. When Rm < ∞, the voltmeter is not ideal and vm < vmi. The difference between vm and vmi is a measurement error caused by the fact that the voltmeter is not ideal.

(b) Express the measurement error that occurs when Rm = 1900 Ω as a percent of vmi.

(c) Determine the minimum value of Rm required to ensure that the measurement error is smaller than 1 percent of vmi.