Why does an ammeter have a low resistance while a voltmeter has high resistance?

I am going to assume that you mean low "resistance" in an open circuit test and are performing this with a multimeter. An ammeter works by place a very small amount of resistance in series with a circuit and then measuring the Voltage drop across the resistance. The Voltage is directly proportional to the current as given in ohms law: E = I x R If you are measuring the resistance through the ammeter it will have a very low resistance and impedance.