Question

Why should an ideal voltmeter have infinite resistance, and an ideal ammeter have no resistance?

Answer 1

This is so that the meter interferes with the circuit being tested as little as possible.

Explanation:

When we use a voltmeter, we are creating a parallel path across a device, which draws a small amount of current away from the device being tested. This impact on the voltage across that device (because V=IR, and we are reducing I). To minimize this effect, the meter should draw as little current as possible - which happens if its resistance is "very large".

With an ammeter, we measure current. But if the meter has any resistance, it will reduce the current in the branch of the circuit we are measuring, and again, we interfere with the measurement we are trying to make. The answer is to have the meter add as little resistance as possible.