Question

I am working on my Physics lab report where it was all about Direct Current Measurement and Ohm’s Law. We had 5 different resistors and had to construct different circuits using a power supply, volt-ohm-milliammeter (VOM) and a digital multimeter to get measurements of resistance, voltage, and current.

Nominal values of resistance and tolerance

Resistor	Nominal Resistance (Ohms)	Tolerance (Ohms)
R1	680	+/- 68
R2	1000	+/- 50
R3	1500	+/- 75
R4	4700	+/- 470
R5	10,000	+/- 500

The above table were the 5 resistors that were used. The first part of the experiment involved measuring values of resistance and uncertainty. I am including parts of the procedure to help with my question so it makes sense.

This is what my lab manual said:

1. Measuring Resistance with the VOM: A resistance measurement with a VOM requires two steps:(1) Connect the red and black leads together and then use the ZERO OHMS knob to adjust the needle to 0 on the OHMS scale. The OHMS scale is at the top and is marked in a nonlinear way with numbers that increase from right to left.(2) Connect the leads to the resistor to be measured and read its resistance on the OHMS scale. The scale reading is multiplied by the factor indicated on the range switch: Rx1, Rx100, or Rx10,000. Whenever the OHMS scale is changed it must be "zeroed" as described above.When the range switch is on a resistance setting, the leads are connected to a battery inside the VOM. For this reason, a resistor should be removed from any circuit that it is in before trying to measure its resistance with the VOM. When a VOM is stored it should not be left on a resistance setting because accidental shorting of the leads would drain current from the internal battery.

2. Measuring Resistance with the Digital Multimeter: Resistance measurement with the digital multimeter does not require initial zeroing. The resistor is connected via leads to the “COM”and “Ω“ sockets. The range switch setting indicates the maximum resistance that can be measured. If a resistance is larger than this maximum, the LED (light emitting diode) display will blink

Now comes the part where I am confused...

Measured values of resistance and uncertainty using VOM

Resistor	VOM Resistance Measurement (OHMS)	Systematic *R (Ohms)
R1	700	?
R2	950	?
R3	1450	?
R4	4700	?
R5	10,000	?

Measured values of resistance and uncertainty using Digital Multimeter

Resistor	Digital Resistance Measurement (OHMS)	Systematic *R (Ohms)
R1	0.704	?
R2	0.991	?
R3	1.503	?
R4	5.18	?
R5	10.34	?

My question is how to calculate uncertainty?

Also, I have to calculate the uncertainty of the actual instruments (VOM and Digital meter) in Volts. The VOM had a voltage of 8.6V with a range of 10V and the digital meter had a voltage of 8.69V. I need to calculate Systematic *V (Volts) and my lab manual is not very helpful

Thank you for reading this and for helping!

Answer 1

The uncertainty in measurement is the amount of error that could occur while measuring a value experimentally. This cannot be found out by doing a single measurement. Taking a number of measurements and calculating the standard deviation on the mean value gives us the uncertainty in measurement.

You should take at least 3 readings. More the no of readings, more accurate the results.

The mean is the average value of N measurements and will give more accurate idea about the value that is being measured.

The standard deviation is the factor by which the measurement has deviated from the mean value.

It is given by

N 1 SD (xi-)2 = N 1 i1

where x_i is the i th measurement and $\bar x$ is the mean.

Here, V = IR.

The error in V is given by

SV/V V(61/1)2R/R)2

Assuming that the value of I has no error,

SV/V R/R

SVSR V/R

Where $\delta R$ is the standard deviation of R