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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
1061840_3128901c85c74601a9b4813f77c4c1a6.PNG


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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