Measuring Direct Current

The moving-coil meter movement can be used to measure any value of direct current by use of shunt resistors in parallel with the movement. A diagram of a basic movement with a shunt resistor is shown in Fig. 5-2. The coil of the meter movement will not handle high currents. The typical current rating of a meter movement ranges from 10 μA to 10 mA. This current rating (I_M) is the amount of current needed to move the pointer to the extreme right side of the scale. This is called full scale. When this current value is smaller, more turns of wire are used for the coil. More turns allow a strong electromagnetic field to develop. As the current rating (I_M) decreases, the resistance (R_M) of the movement increases because of the greater length of wire. You must know the values of I_M and R_M to design a meter circuit that will measure currents higher than the value of I_M.

A shunt resistor is placed in parallel with the meter movement, as shown in Fig. 5-2. Some of the current flowing through the external circuit is “shunted” through the resistor. For this reason the resistor is called a shunt resistor (R_SH). The value of shunt resistance must be precisely calculated. Shunt resistance produces conditions that allow measurement of ranges of current above the value of the meter movement. The value of shunt resistance is found with the following formula:

$R_{\mathrm{SH}}=\frac{I_M\times R_M}{I_{\mathrm{SH}}}$

where R_SH is the shunt resistance in ohms, I_M is the full-scale current of rating of the meter movement in amperes, R_M is the resistance of the meter movement in ohms, and I_SH is the current flow through the shunt resistor in amperes.

For example, a 1.0 mA, 100 Ω meter movement can be used to measure 10 mA. The shunt resistance value is found as follows:

$\begin{array}{c}{R}_{\mathit{SH}}=\frac{I_{\mathrm{M}}\times R_{\mathrm{M}}}{I_{\mathrm{SH}}}\\ =\frac{0.001\times 100}{0.009}\\ =11.11\Omega \\ 1\mathrm{mA}=0.001\mathrm{A}\\ 9\mathrm{mA}=0.009\mathrm{A}\end{array}$

The value of I_SH is 9 mA (0.009 A), or 10 mA – 1 mA = 9 mA. This amount of current must be shunted through the shunt resistor. At the maximum current of the 10 mA range, I_M equals 1.0 mA. A multirange ammeter is designed with several values of shunt resistance and a switching arrangement, as shown in Fig. 5-3. Multirange meters usually have only one scale. They are read directly or have a multiplying factor so that the scale may easily be read for each range. Scales are discussed in unit 2. This type of scale is called a linear scale. It has the same distance between all division marks.

Measuring DC Voltage

Hand-deflection meter movements are another way to measure dc voltage. Meter movements respond to current flow through the electromagnetic coil. As voltage increases, current increases in the same proportion. Voltage values also produce accurate readings on a calibrated meter scale. To measure voltage, a resistor is placed in series with the meter movement. This resistor, shown in Fig. 5-4, is called a multiplier resistor. The purpose of the multiplier is to adjust the value of current across the meter movement. At a certain voltage value (I_M × R_M), full-scale deflection (V_FS) on the meter scale occurs. The formula to find full-scale deflection is as follows:

$V_{\mathrm{FS}}=I_{\mathrm{M}}\times R_{\mathrm{M}}$

A range of dc voltage from 0 to 10 V can be measured with 1.0 mA, 100 Ω meter movement. With 1.0 mA flowing through the 100 Ω meter movement (full scale), 0.1 V is applied across the meter movement (V_FS = 1 mA × 100 Ω = 0.1 V). To measure 10 V at full scale, a multiplier resistance is added in series with the meter movement to drop 9.9 V. This value is found with the following formula:

$\begin{array}{c}{R}_{\mathit{mult}}=\frac{V_{\mathit{mult}}}{I_T}\\ =\frac{9.99}{0.001}\\ =9900\mathbf{\Omega }\end{array}$

Another way to find the value of a multiplier resistance is to calculate the total resistance in the circuit. The values for the circuit with 10 V applied are found as follows:

$\begin{array}{c}{R}_T=\frac{V_T}{I_T}\\ =\frac{10\mathrm{V}}{0.001\mathrm{A}}\\ =10,000\mathbf{\Omega }\end{array}$

The total resistance of the circuit is R_T = R_M + R_mult so

$\begin{array}{c}{R}_{\mathit{mult}}=R_T-R_M\\ =10,000\mathbf{\Omega }-100\mathbf{\Omega }\\ =9900\mathbf{\Omega }\end{array}$

A switching arrangement is used for several voltage ranges that use the same meter movement. A switching arrangement for a multirange voltmeter is shown in Fig. 5-5.

An important characteristic of meters is sensitivity. The sensitivity of a meter increases as the current rating (I_M) decreases. Voltmeters are connected in parallel with a circuit to measure voltage. Part of the circuit current flows through the meter to make the needle deflect. The current that flows through the meter should be very small. More sensitive meters draw less current from the circuit. Sensitivity is measured in ohms per volt and is equal to 1/I_M. Remember that I_M is the current required for full-scale deflection of the meter. A 1 mA movement would have an ohms per volt rating of 1/0.001, or 1000 Ω/V. This means that the meter would have 1000 Ω of resistance for its 1 V range. Sensitivities of meter movements range from as low as 100 Ω/V to as high as 200,000 ΩV. Low-sensitivity meters should not be used for making accurate measurements.

Measuring Resistance

Resistance can be measured with a meter movement. An ohm-meter circuit is shown in Fig. 5-6a.The resistance to be measured is connected in series with the meter circuit. A 1.5 V cell is used to supply current to the meter circuit. The scale of the meter is calibrated so that the movement of the pointer indicates a value of resistance. When the meter probes are touched together, the meter pointer is adjusted to full scale. An ohms scale is shown in Fig. 5-7a. The full-scale mark (right side) indicates zero resistance. As higher values of resistance are measured, less current flows through the meter circuit. The ohmmeter pointer deflects less for higher resistance values. The ohms-adjust control is a potentiometer used to adjust the meter pointer. An ohmmeter must be zeroed before measurements are made. The pointer is adjusted to the zero on the scale when the probes are touched together. The purpose of the ohms-adjust control is to allow accurate measurements as the voltage of the battery in the circuit changes. The left side of the scale indicates infinite resistance. This is an open circuit that has no current flow.

In the ohmmeter circuit of Fig. 5-6a a 1.0 mA, 100 Ω meter movement is used. A value of 900 Ω for the current-limiting resistor (R_lim) is calculated in Fig. 5-7b. The total resistance of the meter circuit will be + R_M + R_lim + R_ohms, or 100 Ω + 900 Ω + 500 Ω = 1500 Ω. When the meter probes are touched together, the total current in the circuit will be 1 mA:

$\begin{array}{c}{I}_T=\frac{V_T}{R_T}\\ =\frac{1.5\mathrm{V}}{1500\mathbf{\Omega }}\\ =0.001\mathrm{A}\\ \left(1.0\mathrm{mA}\right)\end{array}$

One milliampere is the current (I_M) for full-scale deflection of the meter. The ohms scale is calibrated to read 0 Ω at the full-scale deflection point of the meter.

The measured resistance that causes half-scale deflection of the meter pointer is equal to the total resistance of the ohmmeter circuit. To measure a 1500 Ω resistance, the resistor is connected between the meter probes. The total circuit resistance is then 3000 Ω. The meter pointer deflects to only one-half of full scale. With twice as much resistance in the circuit, there is only half as much current. The center of the ohms scale is marked 1500 Ω, as shown in Fig. 5-7b.

If the 3000 Ω resistance is measured, the total circuit resistance is 4500 Ω. This is three times the resistance of the meter circuit. The current in the circuit is then only one-third of the full-scale current (.33 mA). The meter pointer deflects to only one-third of full scale when 3000 Ω is measured. The point on the ohms scale for 3000 Ω is marked. The amount of current can be calculated for any value of measured resistance. The ohms scale is marked according to the current value. The table in Fig. 5-7b shows some values used to calibrate the ohms scale of a meter. This type of scale is called a nonlinear scale. It has division marks that are farther apart on the right than on the left.

There are limits to the amount of resistance an ohmmeter can measure. Several values can be measured with a multirange ohmmeter that has a small battery (usually 1.5 V) for the × 1 and × 100 ranges and a larger battery (usually 9 or 30 V) for ranges of × 1000 and higher.

Multifunction meters (multimeters) usually are designed to measure voltage, current, and resistance. Most hand-deflection analog meters have one meter movement with internal circuits to make many types of measurements. A rotary switch often is used for multimeters to select the quantity to be measured and the proper range.

Measuring Electric Power

Electric power is measured with a wattmeter. A meter movement called a dynamometer is used for most wattmeters. Figure 5-8 shows a meter movement that has two electromagnetic coils. One coil, called the current coil, is connected in series with the circuit to be measured. The other coil, called the potential coil, is connected in parallel with the circuit. The strength of each electromagnetic field affects the movement of the meter pointer. The operating principle of this movement is like that of the moving-coil type. The main difference is that an electromagnetic field rather than a permanent magnet field surrounds the moving coil. DC power is found by means of multiplying voltage and current (P = V × I). AC power is found by means of multiplying voltage, current, and the power factor (pf) of the load (P = V × I × pf). The true power of an ac circuit is read with a wattmeter. When a load is either inductive or capacitive, the true power is less than apparent power (V × I). The true power is the actual power converted by the load.

Measuring Electric Energy

Wattmeters with dynamometer movements are used to measure electric power. They monitor the voltage and current in a circuit. They are used to measure the electric power converted by a load. The amount of electric energy converted into mechanical energy by a motor load is measured by means of connecting a wattmeter to the motor circuit.

The amount of electric energy used over a period of time is measured with a watt-hour meter. A watt-hour meter normally has a small motor inside. The speed of the motor increases as more current passes through it. The rotor is an aluminum disk and is connected to a numerical display. The display indicates the number of kilowatt-hours of electric energy used. Other types have a numerical display of actual kilowatt-hours used.

Watt-hour meters are connected between the power lines coming into a building and the branch circuits inside the building. The electric energy used by a building must pass through the kilowatt-hour meter. The operation of a watt-hour meter is similar to that of a wattmeter. A voltage coil is connected in parallel with power lines to monitor voltage. A current is placed in series with one line to measure current. The voltage and current of the system affect the speed of the aluminum disk. A watt-hour meter is similar to an ac induction motor. This stator is an electromagnet that has two sets of windings: the voltage windings and the current windings. The field developed in the voltage windings causes current to be induced into the aluminum disk. The speed of the disk increases when the voltage or current of the system increases. Because voltage usually stays the same, the speed of the disk increases as current increases. This causes the number display to increase. Watt-hour meters are used to monitor the true power converted in a system over a period of time.

Measuring Three-phase Electric Power

It often is necessary to monitor the three-phase power used by industrial and commercial buildings. A combination of single-phase wattmeters can be used to measure three-phase power, as shown in Fig. 5-9. The method shown is not practical. The sum of the meter readings is used to determine the total power of a three-phase power system. A meter called a three-phase wattmeter is used to measure the true power of a three-phase system. The power indicated on the meter depends on the voltage and current of all three phases of the system. Three-phase watt-hour meters are available. They contain three aluminum disks to monitor the three-phase power used by a system over a period of time. The rotation of the shaft is caused by a combination of the power of each phase. The kilowatt-hour display increases as the three-phase power converted by the system increases.

Measuring Power Factor

Power factor is the ratio of the measured true power of a system to the apparent power (volts × amperes). A wattmeter, a voltmeter, and an ammeter may be used to find the power factor of a system. The power factor can be found as pf = W/VA. It is more convenient to use a power factor meter when power factor must be measured.

The circuit of a power meter is shown in Fig. 5-10. A power factor meter is similar to a wattmeter. It has two armature coils that rotate because of their electromagnetic field strengths. The armature coils are mounted on the same shaft. They are placed about 90° apart. One coil is connected across the power line in series with a resistance (R). The other coil is connected across the line in series with an inductance (L). The resistor in series with the coil produces a magnetic field from the in-phase part of the power. The inductor in series with the other coil produces a magnetic field caused by the out-of-phase part of the power. The scale of the meter is calibrated to measure power factors of 0 to 1.0, or 0 to 100%.

Measuring Power Demand

A power-demand meter is an important instrument for industries and large commercial buildings. Power demand is found with the following formula:

$\mathrm{Power}\mathrm{demand}=\frac{\mathrm{peak}\mathrm{power}\mathrm{used}\left(\mathrm{kW}\right)}{\mathrm{average}\mathrm{power}\mathrm{used}\left(\mathrm{kW}\right)}$

Power demand is important because it shows the ratio of average power used to the peak value that a utility company must supply. Power demand usually is calculated over 15-, 30-, or 60-min intervals. It may be converted into longer periods of time.

The utility company may penalize industries and businesses if their peak power demand is far greater than their average demand. This is called a demand charge. Power-demand meters help companies use their electric power more effectively. High peak demand means the equipment used for power distribution must be larger. The closer the peak demand is to the average demand, the more efficient is the power system.

Measuring Frequency

Another important measurement is frequency. The frequency of the power system must remain the same at all times. Frequency refers to the number of cycles of voltage or current that occur in a given period of time. The international unit used to measure frequency is the hertz (Hz). One hertz equals one cycle per second. A table of frequencies is shown in Table 5-1. The standard power frequency in the United States is 60 Hz. Some countries use 50 Hz.

Frequency is measured with several different types of meters. An electronic counter is used to measure frequency. Vibrating-reed frequency meters often are used. An oscilloscope also is used to measure frequency. Graphic recording instruments can be used to give a visual display of frequency over a period of time. The power industry, for example, must monitor the frequency of its alternators at all times.

Ground-Fault Indicators

A ground-fault indicator is used to locate faulty grounding of equipment or power systems. Equipment must be properly grounded. A ground-fault indicator is used to check for faulty grounding. Several grounding conditions exist that might be dangerous. Faulty conditions include (1) hot and neutral wires reversed, (2) open equipment-ground wires, (3) open neutral wires, (4) open hot wires, (5) hot and equipment grounds reversed, and (6) hot wires on neutral terminals. Each of these conditions presents a serious problem. Proper wiring eliminates most of these problems. A check with a ground-fault indicator assures safe and efficient electric wiring in a building.

Measuring High Resistance

A megohmmeter is used to measure very high resistances. These resistances are beyond the range of most ohmmeters. Megohmmeters are used to check the quality of insulation on electric equipment in industry. The quality of insulation of equipment varies with age, moisture content, and applied voltage. Megohmmeters are similar to most ohmmeters. They have hand-crank, permanent-magnet dc generators rather than batteries as voltage sources. The operator cranks the dc generator while making a test. Insulation tests should be performed on all power equipment. Insulation breakdown causes equipment to fail. Insulation resistance value can be used to determine when equipment has to be replaced or repaired. A decrease in insulation resistance over time means that a problem might soon exist.

Clamp-on Meters

Clamp-on meters are used to measure current in power lines. They are used to check current by means of clamping around a power line. They are easy to use for maintenance and testing of equipment. The meter is simply clamped around a conductor. Current flow through a conductor produces a magnetic field around the conductor. The magnetic field induces a current into the iron core of the clamp-on part of the meter. The meter scale is calibrated to indicate current flow. An increase in current flow through a power line causes the current induced into the clamp-on part of the meter to increase. Clamp-on meters usually have voltage and resistance ranges to make them more versatile.

Wheatstone Bridge

A Wheatstone bridge is a comparison instrument. The circuit of a Wheatstone bridge is shown in Fig. 5-11. A voltage source is used with a sensitive zero-centered movement and a circuit called a resistance bridge. The resistance circuit has an unknown external resistance (R_x), which is the resistance to be measured. Resistor R_s is the known “standard” resistance. R_s is adjusted so that the current path of R_x and R_s is the same value as the path formed by R₁ and R₂. No current flows through the meter at this time. The meter indicates zero current. This is called a null condition. The bridge is said to be balanced. The value of R_s is marked on the instrument to compare with the value of R_x. Resistors R₁ and R₂ are called the ratio arm of the bridge circuit. The value of the unknown resistance (R_x) is found with the following formula:

$R_x=\frac{R_1}{R_2}\times R_s$

Wheatstone bridges are used to measure resistance with precision. Other comparison instruments are based on the Wheatstone bridge principle. Comparison instruments are used to compare unknown quantities with known quantities in the circuits of the instruments.