Although an ideal voltmeter has an infinite internal resistance, this theoretica

Question

Although an ideal voltmeter has an infinite internal resistance, this theoretical ideal is usually not met in practice. The voltmeter in the Figure has an internal resistance of 9 x 109 ? and is used to measure the voltage across the resistor R2 as shown. Attaching this non-ideal voltmeter decreases the voltage across R2. Calculate the magnitude of this decrease using an emf of 18 V and R1 = R2 = 300 k?.

Explanation / Answer

Without Voltmeter Voltage across R2,V1 = E*(R2)/(R1+R2) = 18*300k/(600k) = 9 V With Voltmeter R2 and Rvolt are in parallel Let the equivalent be R2net (1/R2net) = (1/R2) + (1/Rvolt) =>R2net = 299990.000 ohm New voltage across R2net V2 = E*R2net/(R1+R2net) = 8.99985 V Decrease in voltage = V2 - V1 = -1.5*10^-4 V -ve indicates decrease

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