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### Measurement of Resistance:

Resistance can be measured by bridge method. Bridge method of resistance measurement consumes time. In order to approximately know the value of resistance of components etc., a direct reading instrument is necessary. This direct reading instrument that indicates the resistance value over a scale is an Ohm-meter.

It uses the Ohm's law in its working. The resistance R in a circuit is given by the ratio of the voltage across the circuit and the current drawn by the circuit. Hence a volt-meter and ammeter can be used to measure the value of resistance in a circuit. A modification of this method gave the ohm-meter of the direct reading type.

There are two types of ohm-meters. They are the series type or backward reading type and the shunt type or forward reading type.

### (a) Backward Reading or Series Type of Ohm-meter:

The arrangement for measuring resistance with the series type of ohm-meter is explained below. It consists of a voltage source (a cell or a battery) a limiting resistor and a moving coil ammeter of the sensitive type. The value of the resistor in series (limiting resistor) is calculated taking the voltage of the source, the full scale deflection current of the basic meter employed and the internal resistance of the basic meter. The value is

Rs = (E/Im) - Rm

Where E = the voltage of the sources
Im = the full scale deflection of ammeter used
Rm = the internal resistance of the ammeter used
T1 and T2 are the test terminals where the external resistance whose value is to be determined will be connected.

Working Principle:

With the series resistance R, in series with the ammeter, when the test terminals are short circuited, the meter will indicate full scale deflection. That is when there is no external resistance the meter indicates full scale deflection, which point on the scale can he marked as zero resistance. When the test terminals are open circuited that is, there is infinite resistance between the test terminals the ammeter reads zero current. Hence the zero point on the scale of the ammeter can he marked as infinite for resistance scale. For all other values of resistance connected between the test terminals the ammeter will indicate a reading which obeys Ohm's law. A graph showing the variation of current for different values of external resistance is shown below Figure. The ammeter can be calibrated in terms of resistance over a scale. The resistance scale will be in the reverse direction of the normal current scale. That is the reason for calling this type of ohm-meter as a backward reading ohm-meter. The zero of current indicates the infinite of resistance. The maximum (F.S.D) current indicates the zero resistance.

For the other values of resistance a finite value of current will be indicated following Ohm's law.
We can be observe that when the external resistance is equal in value to the total resistance of the ohm-meter, the ohm-meter indicates half scale deflection, Rh. That is when the ammeter's internal resistance plus the series limiting resistance value, is equal to the externally connected resistance the ammeter gives an indication of the half scale reading or half of the full scale current Rh = Rm + R1.

This point is important in the design of this ohm-meter. These ohm-meters will be designed for a given mid-scale reading. The scale is non-uniform. However the scale is clear upto the mid-scale reading but gets crowded after mid-scale reading as the final value of resistance is infinity. The maximum value of resistance that can be measured with this ohm-meter is fixed as a percent of the full scale deflection. Beyond this value there will be no scale marking, excepting the final infinity mark at the end of the scale. Usually this maximum value of resistance is marked at 1% of the full scale deflection current. The value of external resistance that gives 1% of full scale deflection will be marked at the point.

As the mid-scale reading of this ohm-meter is the internal resistance of the ohm-meter, values of resistance below the mid-scale resistance value can be measured easily than values greater than mid-scale resistance value. Therefore this type of ohm-meter is useful in measuring low to medium values of resistances to satisfactory accuracy.

The resistance indicated by this meter will be accurate only when the reference voltage of the cell or battery used is constant throughout. The battery voltage will not be constant when it is on use, as the battery discharges. Hence the ohm-meter will give inaccurate readings as the battery ages. To avoid this zero correction circuits can be provided.

### (b) Zero Adjustment of Series Type Ohm-meter:

One method of obtaining the zero adjustment is to split the series multiplier resistance into two parts, one as a fixed value and the other a variable resistance. Such an arrangement explained below. The value of the variable resistance and fixed value can be determined as follows.

Let the battery voltage be E volts

the internal resistance of the ammeter be Rm ohm and the full scale deflection current of ammeter be 50 μA.
the internal resistance of the ammeter be 2000 Ω
the battery voltage be 1.5 V on full charge.

When the test terminals are short circuited i.e., when there is no external resistance; the value of series resistor will be

1.5 V/50 µA = 30 kΩ – 2 kΩ = 28 kΩ.

Assuming a 10% drop of the battery voltage on use before replacement the series resistance required after discharging to 1.35 V (1.5 V — 0.15 V).

1.35 V/50 μA = 27 kΩ — 2 kΩ = 25 kΩ.

So the maximum value of the series resistor is 28 kΩ and minimum value is 25 kΩ. Therefore a fixed value of 25 kΩ and a variable resistance of 4.7 kΩ can be connected in series as shown in the circuit above. With the new battery the 4.7 kΩ variable resistor will be adjusted to offer only 3 kΩ such that the ammeter gives full scale reading. As the battery looses voltage the variable resistance can be adjusted to further and further lower values of resistance to give full scale deflection. When the battery voltage falls below 1.35 V it is to be replaced.

In this arrangement it can be clearly seen that the calibration of the ohm-meter's scale changes with the adjustment of the zero adjuster. This gives error of 10% showing a mid-scale reading of 30 kn when the battery is new, and 27 kΩ when the battery discharges to 10% of its value.

The second method is to include a shunt resistance across the ammeter and to adjust the value of the shunt to obtain full scale deflection. This method is better than adjusting the series resistance value, as it does not bring large change in calibration. The series type ohm-meter indicates the value of its internal resistance on its mid-scale. Hence designing an ohm-meter's series resistance and shunt for zero adjustment will take this factor into account.

### (c) Applications and Limitations:

Many of the portable multimeters employ this type of ohm-meter circuit. This circuits will be useful in measuring medium values of resistances. The shunt type of zero adjustment will not completely compensate for the drop of the battery voltage, but will give reasonably good compensation. The range of the ohm-meter can he increased by providing required shunts, to cover the required resistance range.

### (d) Shunt Type or Forward Reading Ohm -meter:

The shunt type of consists or a battery a series resistance connected to a basic meter. The arrangement is such that limiting resistance with the battery will circulate the full scale deflection current through the basic meter. The test terminals are taken across the basic meter. The circuit arrangement is shown in Figure.
When the test terminals T1 and T2 are shorted, i.e., when the external resistance Rx is zero, the meter indicates zero current as all the current will be by passed by the short-circuited path of T1 and T2. Therefore this point can be marked as zero for resistance scale.

When the test terminals are open i.e., when the external resistance is infinite, the meter indicates the full scale current. This point on the scale can be marked as infinite for resistance. For other values of resistance connected across the test terminals the meter indicates in proportion to the current drawn by the external resistance connected across test terminals.

### (e) Scales of Shunt and Series Type of Ohm-meters:

The following figure illustrates the scales of both the series and shunt type of ohm-meters Figure. In both the cases the mid-scale reading is indicated. Observation of the scales will show that the series type of ohm-meter is useful for medium values of resistances. Providing additional battery and shunts the series type ohm-meters range can be modified to suite requirements. Thus multirange ohm-meters can be manufactured.
The scale of the shunt type ohm-meter will indicate its competance in measuring low values of resistances extending its utility to measure fractions of an ohm. Both the scales are non-uniform scales.