Galvanometer, Ammeter & Voltmeter

PHYMagnetic Dipole & Instruments

A moving-coil galvanometer deflects by $\theta = (NBA/k)I$ , making deflection proportional to current. It is converted into an ammeter by a low-resistance shunt in parallel and into a voltmeter by a high resistance in series.

ISC numericals ask for the shunt or series resistance for a given range, and for the current sensitivity from the coil parameters. The recurring conceptual point is the distinction between current sensitivity and voltage sensitivity.

Galvanometer deflection and current sensitivity

\theta = \dfrac{NBA}{k}\,I, \qquad S_I = \dfrac{\theta}{I} = \dfrac{NBA}{k}

N

turns,

B

field,

A

coil area,

k

torsion constant;

S_I

is deflection per unit current.

Shunt for an ammeter of range

I

S = \dfrac{I_g\,G}{I - I_g}

I_g

full-scale galvanometer current,

G

galvanometer resistance,

I

desired full-scale ammeter reading,

S

shunt in parallel.

Series resistance for a voltmeter of range

V

R = \dfrac{V}{I_g} - G

V

desired full-scale voltage,

I_g

full-scale current,

G

galvanometer resistance,

R

high resistance in series.

Voltage sensitivity

S_V = \dfrac{\theta}{V} = \dfrac{S_I}{G} = \dfrac{NBA}{kG}

S_V

deflection per unit voltage across the galvanometer of resistance

G

An ammeter must have very low effective resistance, so a small shunt $S$ is connected in parallel; an ideal ammeter has zero resistance.
A voltmeter must have very high resistance, so a large $R$ is connected in series; an ideal voltmeter has infinite resistance.
Current sensitivity $S_I=NBA/k$ rises with turns $N$ , field $B$ and area $A$ , and falls with stiffer suspension (larger $k$ ).
Voltage sensitivity $S_V=S_I/G$ ; increasing $N$ raises $S_I$ but also raises $G$ , so $S_V$ may not increase — they are not the same thing.
The full-scale current $I_g$ and galvanometer resistance $G$ are the fixed instrument data; the shunt or series resistor is then computed for the chosen range.
After shunting, the effective ammeter resistance is the parallel combination $GS/(G+S)$ , which is small.
Keep all currents in the same unit ( $\mathrm{mA}\to\mathrm{A}$ ) before substituting; e.g. $5\ \mathrm{mA}=5\times10^{-3}\ \mathrm{A}$ .

Where the marks go

Swapping the connections: putting the shunt in series or the series resistor in parallel.
Mixing milliamps and amps in the shunt/series formulas, giving wrong resistance values.
Assuming current sensitivity and voltage sensitivity always increase together — $S_V=S_I/G$ , so raising $N$ raises $G$ too.
Forgetting to subtract $G$ in the voltmeter formula $R = V/I_g - G$ .

How the board asks it

Numericalshunt for an ammeter
A galvanometer of resistance $G = 50\ \Omega$ gives full-scale deflection for a current $I_g = 5\ \mathrm{mA}$ . Calculate the value of the shunt resistance required to convert it into an ammeter reading up to $5\ \mathrm{A}$ .
Derive / proveseries resistance conversion formula
A galvanometer of resistance $G$ gives full-scale deflection for current $I_g$ . Obtain an expression for the resistance $R$ that must be connected in series to convert it into a voltmeter of range $0$ to $V$ volts.
Distinguishcurrent sensitivity vs voltage sensitivity
Distinguish between the current sensitivity and the voltage sensitivity of a moving-coil galvanometer, and explain why increasing the number of turns $N$ need not increase the voltage sensitivity.
Give reasonsideal ammeter and voltmeter resistance
Account for the following: an ammeter is connected in series and should have a very low resistance, whereas a voltmeter is connected in parallel and should have a very high resistance.
Define / statecurrent sensitivity from coil parameters
Define the current sensitivity of a moving-coil galvanometer and state two factors on which it depends.
Applicationeffective ammeter resistance $GS/(G+S)$
A galvanometer is converted into an ammeter using a shunt $S$ . Explain how its effective resistance changes and why this makes it suitable for connecting in series in a circuit.

Practise this topic

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Written for Sublevo. Question text quoted anywhere in these notes is the Council’s and carries its year and paper; the board’s own diagrams are not reproduced.