Most multimeters have at least three input terminals:

• COM (Common): Always connect the black probe here
• V/Ω/Hz: For voltage, resistance, frequency, and continuity measurements (red probe)
• mA/μA: For small current measurements up to about 500mA (red probe)
• 10A: For larger current measurements, usually up to 10A (red probe)

Note: Never connect probes to current terminals when measuring voltage or resistance!

Ohm's Law states that:

$V = I \times R$

Where:

• $V$ is voltage in volts (V)
• $I$ is current in amperes (A)
• $R$ is resistance in ohms (Ω)

Rearranging for resistance: $R = \frac{V}{I}$

The percentage difference can be calculated using:

$\text{Difference}(\%) = \frac{|\text{Measured} - \text{Expected}|}{\text{Expected}} \times 100\%$

Example: If you expected 220Ω but measured 228Ω:

$\text{Difference}(\%) = \frac{|228 - 220|}{220} \times 100\% = 3.64\%$

This is within the 5% tolerance, so the resistor is working as expected.

For a series circuit with resistors, the voltage across each resistor follows the voltage divider rule:

$V_{R} = V_{total} \times \frac{R}{R_{total}}$

Where:

• $V_{R}$ is the voltage across a specific resistor
• $V_{total}$ is the total voltage supply
• $R$ is the resistance of the specific resistor
• $R_{total}$ is the total resistance of the circuit

For example, in a circuit with 9V supply and resistors of 220Ω and 1kΩ in series:

$R_{total} = 220Ω + 1000Ω = 1220Ω$

$V_{220Ω} = 9V \times \frac{220Ω}{1220Ω} = 1.62V$

$V_{1kΩ} = 9V \times \frac{1000Ω}{1220Ω} = 7.38V$

For a sinusoidal AC signal, the RMS voltage is related to the peak voltage by:

$V_{RMS} = \frac{V_{peak}}{\sqrt{2}} \approx 0.707 \times V_{peak}$

And the peak-to-peak voltage is:

$V_{peak-to-peak} = 2 \times V_{peak}$

Example: Standard US household power is approximately 120V RMS, which means:

$V_{peak} = 120V \times \sqrt{2} \approx 170V$

$V_{peak-to-peak} \approx 340V$

For an AC circuit with a resistive load, current can be calculated using Ohm's Law:

$I = \frac{V}{R}$

Example: For a 12V AC source connected to a 120Ω resistor:

$I = \frac{12V}{120Ω} = 0.1A = 100mA$

Note: For reactive components like capacitors and inductors, the calculation is more complex and involves impedance rather than simple resistance.

Percentage error can be calculated as:

$\text{Error}(\%) = \frac{|\text{Experimental} - \text{Theoretical}|}{\text{Theoretical}} \times 100\%$

For multiple measurements, you can calculate the average error:

$\text{Average Error}(\%) = \frac{\sum \text{Error}(\%)}{n}$

Where $n$ is the number of measurements taken.

Sources of error might include:

• Instrument precision limitations
• Contact resistance in connections
• Component tolerance variations
• Temperature effects on resistance
• Loading effect of the meter itself