A voltmeter resistance and an ammeter resistance are connected to measure a resistance R, using a circuit as shown in the figure. The resistance is given by , where V is the voltmeter reading and i is the current in the resistor R. Some of the current registered by the ammeter goes through the voltmeter so that the ratio of the meter readings gives only an apparent resistance reading . We have to show that R and are related by

Note that as

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Let the resistance of the voltmeter be . As the voltmeter is connected in parallel with the resistance R , currents flowing through the voltmeter and flowing through the resistance R are related as

The measured resistance

Therefore, we have

We note that as