# The voltmeter shown in figure reads 18 V across the 50 Ω resistor. Find the resistance of the voltmeter.

Concepts/Formula used:

Ohm’s Law:

Potential Difference (V) across a resistor of resistance R when current I passes through it is given by Ohm’s law:

Kirchhoff’s junction rule:

The sum of currents entering a junction is equal to the sum of currents leaving it.

Kirchhoff’s loop rule:

The sum of potential differences around a closed loop is zero.

Let us call the 24Ω resistance be R1 and 50Ω R2 . Let the resistance of voltmeter be RV .

It is given that the voltage across the voltmeter, V = 18V.

The given circuit can be drawn and labelled as follows:

Applying Kirchhoff’s loop rule,

Using Ohm’s law,

The potential difference across voltmeter and R2 is the same as they are in parallel.

Using Ohm’s law again,

Using Kirchhoff’s junction rule at X,

Finally, using Ohm’s law for the voltmeter, we get

Hence, the voltmeter has resistance 130Ω.

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