Loaded Voltage Divider Ideally, a voltmeter has infinite internal resistance and

Question

Loaded Voltage Divider Ideally, a voltmeter has infinite internal resistance and can be placed across any device to read the voltage without affecting the result. A particular digital multimeter (DMM) is connected across the circuit shown in the Figure below. The expected voltage was 5.73 V. However, the DMM reads 3.81 V. The large, but finite, internal resistance of the DMM was "loading" the circuit and causing a wrong measurement to be made. Find the value of the internal resistance R_M of this DMM. The value of R_M (Mega-Ohms) is

Explanation / Answer

Parallel combination of 6.3 and RM will be,
R' = 6.3*RM / (6.3+RM)

V across RM = V across R'
=R'*10 / (R'+4.7)
3.81 = {6.3*10*RM / (6.3+RM)} / {(6.3*RM / (6.3+RM) + 4.7)}
3.81 = 63*RM / (6.3*RM + 4.7*6.3 + 4.7*RM)
3.81 = 63*RM / (11*RM + 29.61)
41.91*RM +112.8 = 63*RM
RM = 5.35 Mohm
Answer: 5.35 Mohm

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