When the DMM is used as a voltmeter, we use it to measure the voltage across a resistor by placing it in parallel with the resistor. What does that tell you about the resistance of the DMM when used a voltmeter?
When the DMM is used as a ammeter, we use it to measure the current through a resistor by placing it in series with the resistor. What does that tell you about the resistance of the DMM when used a ammeter?
When the DMM is used as voltmeter it has very high resistance to ensure that it's connection do not alter flow of current in the circuit. If it has low resistance and connected in parallel across any load then all current in circuit will choose lower resistive path to cause it's circuit to be damaged. So the DMM when connected as voltmeter has very high resistance.
When the DMM is used as ammeter it has very low resistance to ensure the correct measurement of current in the circuit.
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