Understanding Resistance Measurement Tools

Two primary methods are employed in resistance measurement: the ammeter/voltmeter approach and the specialized megohmmeter. The ammeter/voltmeter method measures resistance by measuring voltage and current across a resistor, though errors can arise based on the connection arrangement. On the other hand, the megohmmeter is specialized for high-resistance measurements. It is available in two versions: the hand-cranked and battery-powered variants, each offering specific advantages for precise resistance assessment in diverse electrical applications.

Image used courtesy of Freepik

Ammeter/Voltmeter Methods

If the voltage across a resistor and the current flowing through it are measured, the resistance value can be calculated by applying Ohm's law. However, an error occurs depending on how the ammeter and voltmeter are connected, and this error may be insignificantly small or large enough to be important.

Consider the arrangement shown in Figure 1(a). Because the voltmeter is connected directly across R_x, it measures the actual resistor voltage. However, the ammeter measures the resistor current I_x and the current I_v that flows through the voltmeter. Using the voltage and current measurements, we can calculate a resistance value as follows:

\[Calculated\,Resistance=\frac{Voltmeter\,Reading}{Ammeter\,Reading}\]

\[R_{X1}=\frac{V_{X}}{I_{X}+I_{V}}\]

Equation 1.

(a) Ammeter measuring I_v + I_x

(b) Voltmeter measuring V_A + V_x

Figure 1. Errors can occur when resistance is measured using an ammeter and voltmeter. To minimize errors, the voltmeter should be connected directly across R_x when R_x is low, and the ammeter should be directly in series with R_x when R_x is high. Image used courtesy of Amna Ahmad

The actual resistance of R_x is R_x = V_x/I_x, so the presence of I_v in the equation introduces an error in the result. If I_v is much smaller than I_x, the error may be insignificant. This requires that I_x be a large current, which is the case when R_x is a small resistance.

Now consider the arrangement illustrated in Figure 1(b), where R_x and the ammeter are in series, and the voltmeter is connected in parallel with the two of them. In this case, the ammeter measures the actual current through R_x, but the voltmeter measures the voltage across R_x plus the voltage across the ammeter. Using these two measurements, the resistance is calculated as:

\[R_{X2}=\frac{V_{X}+V_{A}}{I_{X}}\]

Equation 2.

Again, the actual resistance of R_x is R_x = V_x/I_x, and consequently, the presence of V_A in Equation 2 produces an error in the result. The error could be insignificant if V_A is much smaller than V_x. This requires that V_x be a large voltage, which means that R_x should be a large resistance.

The voltmeter should be connected directly across R_x for the greatest accuracy when R_x has a small resistance. For the greatest accuracy when R_x has a large resistance, the ammeter should be connected directly in series with R_x. The correct arrangement can be easily determined by first connecting the ammeter in series with R_x, then observing the ammeter reading with the voltmeter temporarily connected directly across R_x [i.e., connected as in Figure 1(a)]. If the ammeter reading is not noticeably altered when the voltmeter is connected, the readings will give an accurate result. When the ammeter reading is noticeably changed by connecting the voltmeter, the voltmeter should be moved to the other side of the ammeter.

Example 1

An ammeter and voltmeter connected as in Figure 1(a) indicate 10 A and 99 V, respectively. When the voltmeter is changed to reconnect the circuit, as in Figure 1(b), the readings become 10 A and 100 V. The ammeter has a resistance of 0.1 Ω. The voltmeter is on its 100 V range and its sensitivity is 20 kΩ/V. Calculate the measured resistance for each case and determine which arrangements give the most accurate result.

Solution

For the circuit of Figure 1(a)

\[R_{X}=\frac{V_{X}}{I_{X}+I_{V}}=\frac{99V}{10A}=9.9\Omega\]

The voltmeter resistance is

\[R_{V}=\frac{20k\Omega}{V}\times(voltmeter\,range)=\frac{20k\Omega}{V}\times100V=2M\Omega\]

\[I_{V}=\frac{V_{X}}{R_{V}}=\frac{99V}{2M\Omega}=49.5\mu A\]

So

\[I_{V}<

For the circuit of Figure 1(b)

\[R_{X}=\frac{V_{X}+V_{A}}{I_{X}}=\frac{100V}{10A}=10\Omega\]

And

\[V_{A}=I_{A}R_{A}=10A\times0.1\Omega=1V\]

In this case, V_A is not much smaller than V_x, so the connection shown in Figure 1(a) gives the most accurate result.

Example 2

The insulation resistance of an electrical cable is to be measured using a 1000 V source, a 1500 V voltmeter with a sensitivity of 10 k/V, and a 500 A ammeter with a resistance of 100. If the insulation resistance is 5 M, determine the measured resistance using the two methods of connecting the instruments.

Solution

Connection (a) 

I_x = 1000 V/5 MΩ = 200 µA

R_v = 1500 V × 10 kΩ/V = 15 MΩ

I_v = 1000 V/15 MΩ = 66.7 µA

Measured R = V/ (I_x + I_v) = 100 V/ (200 µA + 66.7 µA) = 3.75 MΩ

Connection (b) 

I_x = 1000 V/ (5 MΩ + 100 Ω) ≈ 200 µA

Measured R = V/I_x = 1000 V/200 µA = 5 MΩ

Megohmmeters for Resistance Measurement

The megohmmeter, commonly referred to as a megger, measures exceptionally high resistances, such as the insulation resistance in electrical cables. To achieve this, a high-voltage source is necessary to pass a measurable current through these resistances. In essence, a megger functions like an ohmmeter but employs a low-current instrument and a high-voltage source. As depicted in Figure 2(a), the voltage is typically generated using a hand-cranked generator, ranging from 100 V to 2.5 kV.

Similar to a low-resistance analog ohmmeter, the megger's scale reflects specific values. When measuring an open circuit, it shows infinity (∞), zero for a short circuit, and half-scale when the unknown resistance matches a standard resistor within the megohmmeter. For other positions on the scale, the deflection is directly proportional to the ratio of the unknown and standard resistors. The instrument's range is adjustable by switching various standard resistor values into the circuit.

Megohmmeters operating on battery power are also available, essentially functioning as ohmmeters for very high resistance values. Figure 2(b) illustrates one such instrument. The battery voltage is typically increased to around 1000 V using electronic circuitry to generate a measurable current through the unknown resistance. The measurement is taken by pressing and holding the power button briefly, an arrangement that reduces the current drain on the battery.

Hand-cranked megohmmeter

Battery-powered megohmmeter

Figure 2. A megohmmeter (megger) is essentially an ohmmeter for measuring very high resistances. A high-voltage source and a low-current meter are required. Image used courtesy of Amna Ahmad

Resistance Measurement Takeaways

Two primary methods for measuring resistance are the ammeter/voltmeter and the specialized megohmmeter approach. The ammeter/voltmeter approach calculates resistance by measuring voltage and current across a resistor, but circuit connections may affect its accuracy. On the other hand, the megohmmeter is specifically designed for high-resistance measurements and is available in two versions: hand-cranked and battery-powered. The hand-cranked megohmmeter operates using a hand-cranked generator to measure high resistances. Conversely, the battery-powered megohmmeter offers convenience and efficiency, enabling accurate measurements while minimizing current drain through a press-and-hold mechanism.