College Physics

Figure 21.28An ammeter (A) is placed in series to measure current. All of the current in this circuit flows through the meter. The ammeter would have the same reading if

located between points d and e or between points f and a as it does in the position shown. (Note that the script capital E stands for emf, andrstands for the internal

resistance of the source of potential difference.)

Analog Meters: Galvanometers

Analog metershave a needle that swivels to point at numbers on a scale, as opposed todigital meters, which have numerical readouts similar to a

hand-held calculator. The heart of most analog meters is a device called agalvanometer, denoted by G. Current flow through a galvanometer,IG,

produces a proportional needle deflection. (This deflection is due to the force of a magnetic field upon a current-carrying wire.)

The two crucial characteristics of a given galvanometer are its resistance and current sensitivity.Current sensitivityis the current that gives afull-

scale deflectionof the galvanometer’s needle, the maximum current that the instrument can measure. For example, a galvanometer with a current

sensitivity of50 μAhas a maximum deflection of its needle when50 μAflows through it, reads half-scale when25 μAflows through it, and so

on.

If such a galvanometer has a25- Ω resistance, then a voltage of onlyV=IR=⎛⎝50 μA⎞⎠(25 Ω)= 1.25 mVproduces a full-scale reading. By

connecting resistors to this galvanometer in different ways, you can use it as either a voltmeter or ammeter that can measure a broad range of

voltages or currents.

Galvanometer as Voltmeter

Figure 21.29shows how a galvanometer can be used as a voltmeter by connecting it in series with a large resistance,R. The value of the

resistanceRis determined by the maximum voltage to be measured. Suppose you want 10 V to produce a full-scale deflection of a voltmeter

containing a25-Ωgalvanometer with a50-μAsensitivity. Then 10 V applied to the meter must produce a current of50 μA. The total resistance

must be

(21.68)

Rtot=R+r=V

I

=10 V

50 μA

= 200 kΩ, or

R=Rtot−r= 200 kΩ − 25 Ω ≈ 200 k Ω. (21.69)

(Ris so large that the galvanometer resistance,r, is nearly negligible.) Note that 5 V applied to this voltmeter produces a half-scale deflection by

producing a25-μAcurrent through the meter, and so the voltmeter’s reading is proportional to voltage as desired.

This voltmeter would not be useful for voltages less than about half a volt, because the meter deflection would be small and difficult to read

accurately. For other voltage ranges, other resistances are placed in series with the galvanometer. Many meters have a choice of scales. That choice

involves switching an appropriate resistance into series with the galvanometer.

Figure 21.29A large resistanceRplaced in series with a galvanometer G produces a voltmeter, the full-scale deflection of which depends on the choice ofR. The larger

the voltage to be measured, the largerRmust be. (Note thatrrepresents the internal resistance of the galvanometer.)

Galvanometer as Ammeter

The same galvanometer can also be made into an ammeter by placing it in parallel with a small resistanceR, often called theshunt resistance, as

shown inFigure 21.30. Since the shunt resistance is small, most of the current passes through it, allowing an ammeter to measure currents much

greater than those producing a full-scale deflection of the galvanometer.

Suppose, for example, an ammeter is needed that gives a full-scale deflection for 1.0 A, and contains the same 2 5- Ω galvanometer with its

50-μAsensitivity. SinceRandrare in parallel, the voltage across them is the same.

TheseIRdrops areIR=IGrso thatIR=

IG

I

=Rr. Solving forR, and noting thatIGis50 μAandIis 0.999950 A, we have

(21.70)

R=r

IG

I

= (25 Ω )

50 μA

0.999950 A

= 1.25× 10 −3 Ω.

756 CHAPTER 21 | CIRCUITS, BIOELECTRICITY, AND DC INSTRUMENTS

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