# multimeter input impedance calculation discrepancies

To measure the input impedance of a multimeter, I have built a voltage divider circuit with equal resistances R1 and R2 and measured the voltage across one of them using the multimeter. Considering that a multimeter is an ideal voltmeter in parallel with a resistor with value equal to input impedance I derived the following equation: $$R_{ii} = \frac{R_1R_2}{(\frac{V_s}{V_{meas}} - 1)R_2 - R_1}$$ The circuit is as shown below:

When I measured the voltage using 10kohm and calculate impedance using the above equation, I get a value of 2.58Mohm but when I repeat the same with 100kohm and 1Mohm I get values close to 9Mohm for input impedance. Why does this discrepancy exist? Please explain with equations if possible.

NOTE: I measured the values of the resistances that I used in the circuit with the multimeter so I get that it is a circular problem with using the multimeter to measure circuit resistances and using the circuit resistances to measure the multimeter impedance, but I am at a loss for measuring the impedance in other ways without involving another meter. Please also give ideas on how to measure the impedance otherwise without the use of a secondary meter.

• sounds like your calculations were wrong with measurement tolerances. Eliminate R2 . – Tony Stewart Sunnyskyguy EE75 Sep 22 '17 at 2:34
• Show your measurements and calculations. – Bruce Abbott Sep 22 '17 at 2:43
• Re-run your 10kilohm calculations with R2 value 1% too high, and 1% too low. – Brian Drummond Sep 22 '17 at 9:53
• Resistance measurements will be independent of meter resistance. A different circuit is used within the meter for each function. – WhatRoughBeast Sep 22 '17 at 15:10