Question

# In the circuit shown here, the ammeter $$A$$ reads $$5$$A and the voltmeter $$V$$ reads $$20$$V.Find the correct value of resistance

Solution

## Voltmeters generally have a very high resistance and $$\therefore$$ a very small amount $$\left(>0 A\right)$$ of current passes through them.Thus,the amount of current flowing as $${I}_{1},$$(current through $$R$$) and $${I}_{2}$$(current through $$V$$) will be $$I=5$$A$$\Rightarrow {I}_{1}+{I}_{2}=5$$$$\therefore {I}_{1}=5-{I}_{2}$$As $${I}_{2}>0$$$$\Rightarrow {I}_{1}<5$$Applying Ohm's law on the LHS of the above inequality,$$\dfrac{20}{R}<5$$ since $${I}_{1}=\dfrac{20}{R}$$$$\Rightarrow \dfrac{20}{5}<R$$$$\therefore R>4\Omega$$$$\therefore$$ the correct value of resistance $$R$$ is slightly greater than $$4\Omega$$Physics

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