# I. DC Voltage Measurement with a Digital Multimeter >[!table] Measured DC Supply Voltages > >| Set Voltage [V] | Measured Voltage [V] | Difference [V] | % Error | >| ---: | ---: | ---: | ---: | >| 1.0 | 0.999 | -0.001 | 0.100% | >| -1.0 | -1.001 | -0.001 | 0.100% | >| 2.0 | 1.999 | -0.001 | 0.050% | >| -2.0 | -1.999 | 0.001 | 0.050% | >| 2.5 | 2.499 | -0.001 | 0.040% | >| -2.5 | -2.499 | 0.001 | 0.040% | >| 4.0 | 3.999 | -0.001 | 0.025% | >| -4.0 | -3.999 | 0.001 | 0.025% | $\text{Mean difference}=-0.00025V$ $\text{Standard deviation}=0.00104V$ The small mean difference and standard deviation indicate that the DMM measurements were precise and closely matched the set PSU voltages. --- To obtain 35V, the 30V and 5V channels of the PSU were connected in series so that their voltages added together. $V_{out}=30V+5V=35V$ >[!table] 35V Series Supply Measurement > >| Measured Voltage [V] | % Error | >| ---: | ---: | >| 35.010 | 0.0286% | --- >[!table] PSU and DMM Voltage Adjustment Comparison > >| Set Voltage [V] | Measured Voltage [V] | % Error | >| ---: | ---: | ---: | >| 5.125 | 5.1246 | 0.00780% | >| 5.126 | 5.1250 | 0.0195% | Both errors are much less than 5%. The small differences are due to the finite resolution and calibration of the PSU and DMM. --- Current through a $220\Omega$ resistor with 5V applied: $I=\frac{V}{R}=\frac{5}{220}=0.0227A=22.7mA$ --- With the PSU set to 5V and a 15mA current limit, the $220\Omega$ resistor would ideally draw 22.7mA. Since this exceeds the current limit, the PSU will enter current-limiting mode and reduce the output voltage. --- When the $220\Omega$ resistor was connected, the measured voltage dropped to approximately 3.17V because the PSU limited the current to 15mA. $V=IR=(0.015)(220)=3.30V$ The measured value was close to the expected current-limited voltage. --- Minimum resistance required to avoid exceeding the 15mA current limit: $R_{min}=\frac{V}{I}=\frac{5}{0.015}=333.3\Omega$ A resistor of approximately $330\Omega$ was used. >[!table] Power Supply and DMM Measurements > >| Instrument | Voltage [V] | Current [A] | >| --- | ---: | ---: | >| Power Supply | 5.000 | 0.015 | >| DMM | 4.991 | 0.015165 | The DMM should be relied on for the more precise measurement because it is designed specifically for measurement and provides greater resolution than the PSU display. # II. Verification of Ohm's Law >[!table] Measured Voltage and Current for $1k\Omega$ Resistor > >| Set Voltage [V] | Measured Current [mA] | >| ---: | ---: | >| 0.0 | 0 | >| 0.5 | 0.5008 | >| 1.0 | 1.001 | >| 1.5 | 1.502 | >| 2.0 | 2.003 | >| 2.5 | 2.503 | >| 3.0 | 3.004 | >| 3.5 | 3.507 | >| 4.0 | 4.008 | >| 4.5 | 4.510 | >| 5.0 | 5.013 | --- <div style="page-break-after: always;"></div> >[!figures] I-V Characteristic of $1k\Omega$ Resistor >![[Pasted image 20260910192104.png|center|500]] The line of best fit is $I=1.0024V-0.0014\text{ mA}$ The slope is $1.0024\text{ mA/V}$ and represents the conductance, $\frac{1}{R}$, of the resistor. $R=\frac{1000}{1.0024}=997.6\Omega$ The linear relationship between current and voltage agrees with Ohm's Law. --- Measured resistance: $R_{DMM}=998.06\Omega$ Expected resistance: $R_{expected}=1000\Omega$ Resistance from the line of best fit: $R_{fit}=997.6\Omega$ The largest difference is between the expected resistance and the best-fit resistance: $\Delta R=1000-997.6=2.4\Omega$ $\%\text{ error}=\frac{2.4}{1000}(100)=0.24\%$ This is a reasonable error because it is small and falls within the resistor's specified tolerance. --- Measured resistance = $998.06\Omega$. The resistor tolerance band is brown, signifying a $\pm1\%$ tolerance. $R_{min}=1000(0.99)=990\Omega$ $R_{max}=1000(1.01)=1010\Omega$ The measured resistance of $998.06\Omega$ and the best-fit resistance of $997.6\Omega$ both fall within the acceptable range of $990\Omega$ to $1010\Omega$. Therefore, the resistor is within its specified tolerance.