Quick Questions for General Physics

Question

1. In using an ammeter, it should be connected in series to the component to be measured. Explain why should the resistance of the ammeter must be equal to zero.
2. In using voltmeter, it should be connected in parallel to the component to be measured. Explain why should the resistance of the voltmeter must have an infinite resistance?

Answer 1

1.

Suppose that you have a circuit with resistance R,

and before inserting the ammeter, there is current I.

That implies voltage IR.

After inserting an ammeter with resistance r,

the total resistance of the circuit becomes R+r, and

the current becomes IR/(R+r).

That causes the ammeter to measure current different from the original I,

by a factor R/(R+r).

The smaller the r, the closer is R/(R+r) to 1, getting a closer approximation to I.

2.

Suppose you want to measure voltage across a resistance R,

and suppose the current flowing through it is I.

That means, the voltage across the resistance is IR.

After adding the voltmeter with resistance r in parallel to R,

the new resistance becomes

Rr/(R+r),

and the voltmeter will measure voltage IRr/(R+r).

That causes the voltmeter to measure voltage different from the original IR

by a factor r/(R+r).

The bigger the r, the closer is r/(R+r) to 1, getting a closer approximation to IR.