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 below has an internal resistance of 10^9 Ohm and is used to measure the voltage across a resistor with R_2 = 130 k Ohm as shown. How much does this nonideal voltmeter affect the circuit? That is, attaching the voltmeter changes the voltage across R_2. What is the fractional change in the voltage across R_2 when the voltmeter is attached? (Find 1 - V_f/V_i, where V_i, V_f are the voltage across R_2 before and after the voltmeter was attached to the circuit, respectively. For simplicity assume R_1 = R_2.)

Explanation / Answer

Here ,

Rin = 10^9 Ohm

R2 = 130 Kohm

when there is voltmeter

USing voltage divider rule for finding the voltage across R2

Vi = E * 130 /(130 + 130)

Vi = 0.50 * E

Now, when the voltmeter is connected

resistance of R2 will be

1/Rf = 1/10^9 + 1/130*10^3

Rf = 129.98 kOhm

USing voltage divider rule for finding the voltage across R2

Vf = E * 129.98/(130 + 129.98)

Vf = 0.49996 * E

Now, for the fractional change

fractional change = 1 - Vf/Vi

fractional change = 1 - 0.49996/0.50

fractional change = 0.00008

the fractional change is 0.00008

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