Analog Meters: Galvanometers

Analog Meters: Galvanometers

Analog meters have a needle that swivels to point at numbers on a scale, as opposed to digital meters, which have numerical readouts similar to a hand-held calculator. The heart of most analog meters is a device called a galvanometer, denoted by G. Current flow through a galvanometer, \({I}_{\text{G}}\), 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 sensitivity is the current that gives a full-scale deflection of the galvanometer’s needle, the maximum current that the instrument can measure. For example, a galvanometer with a current sensitivity of \(\text{50 μA}\) has a maximum deflection of its needle when \(\text{50 μA}\) flows through it, reads half-scale when \(25 \mu A\) flows through it, and so on.

If such a galvanometer has a \(2\text{5-}\Omega \) resistance, then a voltage of only \(V=\text{IR}=(\text{50 μA})(\text{25 Ω})=1\text{.}\text{25 mV}\) produces 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

This figure shows how a galvanometer can be used as a voltmeter by connecting it in series with a large resistance, \(R\). The value of the resistance \(R\) is determined by the maximum voltage to be measured. Suppose you want 10 V to produce a full-scale deflection of a voltmeter containing a \(2\text{5-Ω}\) galvanometer with a \(\text{50-μA}\) sensitivity. Then 10 V applied to the meter must produce a current of \(\text{50 μA}\). The total resistance must be

\({R}_{\text{tot}}=R+r=\cfrac{V}{I}=\cfrac{\text{10}\phantom{\rule{0.25em}{0ex}}\text{V}}{\text{50 μA}}=\text{200}\phantom{\rule{0.25em}{0ex}}\text{k}\Omega , or\)

\(R={R}_{\text{tot}}-r=\text{200 kΩ}-\text{25}\phantom{\rule{0.25em}{0ex}}\Omega \approx \text{200}\phantom{\rule{0.25em}{0ex}}\text{k}\Omega .\)

(\(R\) is 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 a \(2\text{5-μA}\) current 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.

A large resistance \(R\) placed in series with a galvanometer G produces a voltmeter, the full-scale deflection of which depends on the choice of \(R\). The larger the voltage to be measured, the larger \(R\) must be. (Note that \(r\) represents 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 resistance \(R\), often called the shunt resistance, as shown in this figure. 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 \(2\text{5-}\Omega \) galvanometer with its \(\text{50-μA}\) sensitivity. Since \(R\) and \(r\) are in parallel, the voltage across them is the same.

These \(\text{IR}\) drops are \(\text{IR}={I}_{\text{G}}r\) so that \(\text{IR}=\cfrac{{I}_{\text{G}}}{I}=\cfrac{R}{r}\). Solving for \(R\), and noting that \({I}_{\text{G}}\) is \(\text{50 μA}\) and \(I\) is 0.999950 A, we have

\(R=r\cfrac{{I}_{\text{G}}}{I}=(\text{25}\phantom{\rule{0.15em}{0ex}}\Omega )\cfrac{\text{50 μA}}{0\text{.}\text{999950 A}}=1\text{.}\text{25}×{\text{10}}^{-3}\phantom{\rule{0.15em}{0ex}}\Omega .\)

A small shunt resistance \(R\) placed in parallel with a galvanometer G produces an ammeter, the full-scale deflection of which depends on the choice of \(R\). The larger the current to be measured, the smaller \(R\) must be. Most of the current (\(I\)) flowing through the meter is shunted through \(R\) to protect the galvanometer. (Note that \(r\) represents the internal resistance of the galvanometer.) Ammeters may also have multiple scales for greater flexibility in application. The various scales are achieved by switching various shunt resistances in parallel with the galvanometer—the greater the maximum current to be measured, the smaller the shunt resistance must be.