DC Ammeter

Figure 1: A dc ammeter consists of a PMMC instrument and a low resistance shunt

WhereRm = internal resistance of the coilRsh = resistance of the shuntIm = full-scale deflection current of the coilIsh = shunt currentI = full-scale current of the ammeter including the shunt

ExampleAn ammeter exists with Rm = 99 Ω and FSD current of 0.1 mA, also Rs = 1 Ω. Determine the total current passing through the ammeter at (a) FSD, (b) 0.5 FSD, (c) 0.25 FSD.

Multirange Ammeter To increase the measuring capacity Protecting the instrument from excessive current flow

Figure 2: Multirange ammeter using switched shunts

Figure 3: An Ayrton shunt used with an ammeter consists of several series-connected resistors all connected in parallel with the PMMC instrument

Precaution of using ammeter

Never connect an ammeter across a source of emf Observe the correct polarity When using a multirange meter, first use the highest current range.

Always use the range that will give you a reading as near to full-scale as possible

DC Voltmeter

Figure 4: A dc voltmeter is made up of a PMMC instrument and a series multiplier resistor.

WhereIm = deflection current of the meterRm = internal resistance of the meterRs = multiplier resistanceV = full-range voltage of the meter

Example

A PMMC instrument with FSD = 100 µA and Rm = 1 kΩ, to be converted into voltmeter. Determine Rs if the voltmeter is to measure 50 V at full scale. Also, calculate the applied voltage when the instrument indicates 0.8 FSD.

Multirange Voltmeter

Figure 5(a): Multirange voltmeter using switched multiplier resistors

Figure 5(b): Multirange voltmeter using series-connected multiplier resistors

Example

A PMMC instrument with FSD = 50 µA and Rm = 1700 Ω is to be employed as a voltmeter with ranges of 10 V, 50 V, 100 V. Calculate required values of multiplier resistors for the above circuits.

Series Ohmmeter

Figure 6: Basic series ohmmeter circuit consisting of a PMMC instrument and a standard resistor (R1)

WhereEb = batteryRx = resistance to be measuredRm = meter resistanceR1 = standard resistor

mx

bm RRR

EI

1

For Rx = 0 Ω, the pointer indicates 0 Ω → max. current will flowFor Rx = ∞, the pointer indicates ∞ → no current will flowPointer position depends on the relationship between Rx and (R1 + Rm)

Example

A series ohmmeter has 1.5 V battery, a 100 µA meter and R1 which makes (R1 + Rm) = 15 kΩ.(a) Determine the instrument indication when Rx = 0 Ω(b) Determine how the resistance scale should be marked at 0.5 FSD, 0.25 FSD and 0.75 FSD.

Ohmmeter with Zero Adjust

Series ohmmeter will operate satisfactorily as long as the battery remains exactly at its value. When the battery voltage falls, the instrument scale is no longer correct. Falling battery voltage can be taken care of by an adjustable resistor connected in parallel with the meter.

Figure 7: An adjustable resistor (R2) connected in parallel with the meter provides an ohmmeter zero control.

The ohmmeter terminals are initially short-circuited and the zero control (R2) is adjusted to give zero-ohms reading.

Example

For the above figure, Eb = 1.5 V, R1 = 15 kΩ, Rm = 50 Ω, R2 = 50 Ω and FSD = 50 µA. Determine the meter reading at 0.5 FSD, and new value of R2 when Eb falls to 1.3 V. Also, determine the meter reading at 0.5 FSD when Eb = 1.3 V.

Ans: 15 kΩ, 68.18 Ω, 15 kΩ

Shunt Ohmmeter - Multirange

Major inconvenience of series ohmmeter: large adjustment of zero control would have to be made.

Using shunt ohmmeter, only zero adjustment is needed.

Figure 8: Circuit, scale and range switch for a typical multirange shunt ohmmeter

Example

(a) In the above figure, calculate Im when Rx = 0 Ω at the range of Rx1. Also, calculate Im when Rx = 24 Ω.(b) With the range of Rx10, calculate Im for Rx = 0 Ω and Rx = 70 Ω.

Ans: (a) 37.5 µA, 18.72 µA; (b) 37.53 µA, 29.04 µA.

Megger

Figure 9: Megger

Measuring very high resistance. It has hand-driven dc generator – supplies high voltage. Coil ‘a’ tends to move the pointer clockwise, and coil ‘b’ tends to

move the pointer counterclockwise. Coil ‘a’ is connected in series with R3 and Rx, and connected

across the generator. Coil ‘b’ is connected in series with R2, and also connected across

the generator. There are no restraining springs – therefore the pointer floats freely.

If the test leads are open-circuited (Rx = ∞), No current flows in coil ‘a’ Current flows in coil ‘b’ Pointer is deflected to infinite resistance

If the test leads are shorted (Rx = 0), Pointer rests at zero because the current in coil ‘a’ is relatively high

comparing to coil ‘b’

If 0<Rx< ∞, Current flows through coil ‘a’, tending to move the pointer clockwise Current will also flow through coil ‘b’, tending to move the pointer

counterclockwise The pointer comes to rest at a position at which the two forces are

exactly balanced