When a high resistance is connected in series with a galvanometer, it becomes a voltmeter. Fig.(i) above shows a high resistance R connected in series with a galvanometer of resistance G. If Ig is the full scale deflection current, then the galvanometer becomes a voltmeter of range 0 – V volts. The require value of series resistance R is given by Voltage for fsd= V fsd = I g R + I g G = I g ( R + G ) = I g Rm , where, R m =meter resistance....... (1) For maximum accuracy, a multimeter is always provided with a number of voltage ranges. This is achieved by providing a number of high resistances in the multimeter as shown in fig. (ii). Suppose the full scale deflection (fsd) current in a galvanometer is 50 A and Rm=50 . [For this we may use a resistance R in series with the galvanometer]. So the voltage for the meter considered here for fsd =50×Rm=50× 50=2500 V = 2.5mV . So this instrument can be calibrated to measure voltage upto this low value for full scale deflection. In order to increase the voltage range, let the series resistor to be used be RS. Here we increase V keeping Ig constant. Then, ( RS + Rm ) I g = Desired voltage range V ............... ...... (2) (2) RS + Rm Desired voltage range = = = n (say) (1) Rm Voltage for fsd RS + Rm = Rm .n RS = Rm (n − 1) In the meter considered here, voltage for fsd = 2.5 mV. 2.5V − 1 = Rm (1000 − 1) = 50 999 In order to increase the range to 2.5 V, RS = Rm (n − 1) = Rm 2.5mV 25V − 1 = Rm (10000 − 1) = 50 9999 In order to increase the range to 25 V, RS = Rm (n − 1) = Rm 2.5mV 250V − 1 = Rm (100000 − 1) = 50 99999 In order to increase the range to 250 V, RS = Rm (n − 1) = Rm 2.5mV 2500V − 1 = Rm (1000000 − 1) = 50 999999 In order to increase the range to 2500 V, RS = Rm (n − 1) = Rm 2.5mV Hence, the meter connected to different series resistors through multi-pole switch acts as a variable range voltmeter as shown in fig.(ii) above. When dc voltages are to be measured, the multimeter switch is turned on to dc position. This puts the circuit as shown in fig.(ii). By throwing the range selector switch S to a suitable position, the given dc voltage can be measured. When ac voltages are to be measured, a full wave rectifier is used as shown in fig. below. The rectifier converts ac into dc to apply to the galvanometer. The desired ac voltage range can be selected by the switch S. When ac voltage is to be measured, the multimeter switch is thrown to ac position. This puts the circuit below in action. By throwing the range selector switch S to a suitable position, the given ac voltage can be measured. It may be mentioned here that ac voltage scale is calibrated in r.m.s. values. Therefore, the meter will give the r.m.s. value of ac voltage under measurement. [Fig.16.3] Multimeter as ammeter
[Fig.16.4] When a low resistance (called shunt) is connected in parallel with a galvanometer, it becomes an ammeter. Suppose the galvanometer has resistance G. Let the fsd current for the meter be 50 A = I g . It means this meter in its unmodified form, can measure current upto 50 A . To increase the range of this meter, let a shunt resistance S is connected in parallel with the galvanometer. Referring to fig.16.4(i), IS S = I gG IS + Ig G I G G G IS G I G = + 1, = + 1, n = + 1 n − 1 = = , S + 1 = + 1, Ig S Ig S S S Ig S Ig S G S= ................................. (1) n −1 Required current range where, n= fsd current Hence to increase the range of the current, we connect a shunt S parallel to the galvanometer; the value of the shunt is given by eqn. (1). G G G = = Thus to increase the range to 0.25 mA, the shunt resistance to be used= S1 = 0.25mA −1 5 −1 4 50A 2.5 mA G G = = 50 , so S 2 = To increase the range to 2.5 mA, i.e. n = 50 − 1 49 50 A 25 mA G G = = 500 , so S2 = To increase the range to 25 mA, i.e. n = 500 − 1 499 50 A G G 2.5 A = 50,000 , so S2 = = To increase the range to 2.5 A, i.e. n = 50A 50,000 − 1 49,999 Hence knowing the value of G and fsd current, one can use the shunt resistance to be used for the desired range. Shunt resistances of different values are connected to the same meter through a multiple switch, which is shown in fig. below. With the help of range selector switch S, any shunt can be put in parallel with the galvanometer. [Fig.16.5] When dc current is to be measured, the multimeter switch is turned on to dc position. This puts the circuit in fig. above in action. By throwing the range selector switch S to a suitable position, the desired dc current can be measured. The multimeter can also be used to measure alternating current. For this purpose, a full-wave rectifier is used as shown in fig. below. The rectifier converts ac into dc for application to the galvanometer. The desired current range can be selected by switch S. By throwing the range selector switch S to a suitable position, the given ac current can be measured. Here, the ac current scale is calibrated in r.m.s. values so that the instrument will give r.m.s. value of alternating current under measurement.
[Fig.16.6] Multimeter as ohm-meter [Fig.16.7] Fig. above shows the circuit of ohm-meter. The multimeter employs its own internal battery. A fixed resistance R (or R1, R2, R3) and a variable resistance ‘r’ are connected in series with the battery and the galvanometer. The resistances R1, R2, R3 decides the ranges [Fig.(ii)] and the variable resistance ‘r’ is for zero-adjustment. The resistance to be measured is connected between the terminals A and B. To use the ohm-meter, terminals A and B are shorted and the resistance ‘r’ is adjusted to give full scale deflection of the galvanometer. Under this condition, the resistance under measurement is zero. Because the needle deflects to full scale, the extreme right of the ohm-meter scale indicates zero ohm of the V resistance scale. Here, I m = .[Fig.(i)] R+r +G When a resistance RX is connected across the terminals A and B, the current in the circuit V = IX = RX + R + r + G Since the current is inversely proportional to the total resistance in the circuit, increasing the value of RX will cause reduction in current. When Rx is extremely high or infinity, current becomes negligibly small or zero. Thus the resistance scale can be calibrated from right to left as zero to infinity, which is opposite to that of an ammeter or voltmeter. In a multimeter, the ohm-meter section on the front panel is usually marked as R×1, R×10, R×100, R×1k as different ranges; it means the reading on the ohm-meter scale is to be multiplied by 1, 10 , 100 or 1k respectively. It may be mentioned here that while using the ohm-meter, each time it is first shorted across AB and ‘r’ is adjusted to bring the meter reading to zero. This calibrates the meter and accommodates any decrease in the terminal voltage of the battery with age. For lower ranges, 1.5 V battery is used while for k range, 15 V battery is used. Sensitivity of a multimeter The resistance offered per volt for full scale deflection of the multimeter when used as voltmeter is known as multimeter sensitivity. Multimeter sensitivity indicates the internal resistance of the multimeter. For example, if the total resistance of the meter is 5000 ohms and the meter is to read 5 volts full scale, then the internal resistance of the meter is 1000 per volt, i.e. meter sensitivity is 1000 per volt. Conversely, if the meter sensitivity is
400 per volt which reads from 0 to 100 V, then meter resistance is 40,000 . Thus, if the meter is to read V volts and Ig is the full scale deflection current, then V Meter resistance= Ig V / Ig 1 = Meter sensitivity= Resistance per volt for full scale deflection= V Ig Multimeter sensitivity indicates the internal resistance of the multimeter. If the sensitivity of a multimeter is high, it means that it has high internal resistance. When such a meter is connected in the circuit to read voltage, it will draw a very small current. Consequently, there will be no change in the circuit current due to the introduction of the meter. Hence it will measure the voltage correctly. On the other hand, if the sensitivity of the multimeter is low, it would cause serious error in voltage measurement. The sensitivity of the multimeters available in the market, range from 5 k per volt to 20 k per volt. Meter protection [Fig.16.8] It is important to provide protection for the meter in the event of an accidental overload. This is achieved by connecting a silicon diode in parallel with the voltmeter as shown in fig.16.8 above. If I is the normal fsd current, a potential difference of IRm is developed across the diode. The circuit is so designed that IRm does not turn on the diode. In case of an accidental overload (say 5I), the voltage across the diode becomes 5 times greater and it is immediately turned on. Consequently, the diode diverts most of the overload current in the same manner as a shunt. Thus the protection of the meter against overload is ensured. VACUUM TUBE VOLTMETER (VTVM) Vacuum tube voltmeter is an electronic device which measures current, voltage and resistance like a multimeter, but it has got the following advantages over a multimeter. (i) A very low or very high resistance can’t be measured accurately with a multimeter. For low resistance, there may be large variation or drift and for high resistance, the calibrations are too close to each other to prevent accurate observation. But a VTVM can measure with reasonable accuracy from 0.1 to few hundred M . (ii) For voltage measurement, the current drain from the circuit under measurement should be minimum. The input impedance of the VTVM is very high, i.e. infinite (>10 M ). So a VTVM draws negligible amount of current from the circuit. This property also makes it more suitable for measurement in low current circuits than ordinary voltmeter or multimeter. (iii) A multimeter is suitable for measurement only in low frequency ac, but a VTVM measures more accurately upto frequencies as high as 100 MHz. (iv) The VTVM possesses the property of amplification. This property permits the input signal to be amplified so that the power to operate the indicating mechanism comes from a source other than the measured circuit. Construction A VTVM uses a current meter, vacuum tubes for differential amplifier and other circuitry arrangements that are commonly used in a multimeter. The basic circuit arrangement of a two tube VTVM is shown in fig. below. It consists of two similar triodes T1 and T2, a dc meter, dc