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Why should the effective resistance of a...

Why should the effective resistance of an ideal ammeter be zero and that of a voltmeter, be infinity?

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The effective resistance of an ideal ammeter should be zero because it should draw the entire current when it is connected in series in the circuit. The resistance of the ideal voltmeter is infinite because it should not draw any current when it is connected in parallel across the circuit component, and hence its introduction should not alter the potential difference to be measured.
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