E84 Lab 1: Multimeter

• Study the schematic diagram of a multimeter shown in the figure below carefully to understand how the multimeter measures both DC and AC voltages, DC currents, and resistances at each of the positions of the rotary switch. Additional information is available here.

• R24 is a potentiometer, a resistor of $10\;K\Omega$ but with an additional terminal which is a piece of metal that can slide along the resistor, so that the resistance between the 3rd terminal and any of the other two is variable between 0 and 10 $K\Omega$. See here for more detailed explanation. This potentiometer is needed to calibrate the Ohmmeter. Specifically, before taking the measurement of a resistance, the potentiometer needs to be adjusted so that the needle points to zero on the resistance scale when the two leads of the multimeter touch each other for zero resistance.

• Understand how the rotary switch works. It is represented by the 24 circles on top of the diagram and the two layers of rectangular shapes above. At each of the positions, the corresponding circle is connected to both of the rectangles, while all remaining circles are not connected to anything. If you still have difficulty understanding this, it should be most helpful if you take a look at the physical parts and the printed circuit board (PCB) in the kit.

• Do all parts specified below. Turn in your answer on paper with all the resistance values before the first deadline.

• Assemble the multimeter in the lab, verify every single position to see if the meter works as expected.

1. Meterhead assembly: (used for all measurements except resistance measurement)
   • When a voltage of $0.1\;V$ or a current of $50\;\mu A$ is applied to the position marked ``$0.1V/50\mu A$'', the meter shows a full scale display. Find the total resistance of the internal circuitry in the multimeter at this position. This information is necessary for understanding the DC voltage and current measurement.

   • Find the needed voltage and current for a full scale display of the meter head assembly (the meter head in series with $R8=680\;\Omega$, in parallel with both $R26=31\;k\Omega$ and $R24+R25=10k+18k=28\;k\Omega$, excluding $R7=240\;\Omega$).

     Also find the over all resistance $R_M$ of the meter head assembly. This information is necessary for understanding the AC voltage and resistance measurement.

   • Find the resistance $R_m$ of the meter-head in series with R8 (excluding R31 and R24 + R25).

2. DC Voltage measurement

   Find the values of R1 through R6 for the 6 scales of DC voltage measurement so that these resistors will indeed allow a full display with $I_m=50\;\mu A$ at the marked DC voltage for each of the 6 position. Note that $R13=3\;k\Omega$ is in series with $R7=240\;\Omega$ and the meter-head assembly with total resistance $R13+R7+R_M=5\;k\Omega$.

3. AC Voltage measurement

   Based on the given values of R14 through R17 for AC voltage measurement (Figure 5 of the manual of the kit) find the total resistance $R_{DM}$ of the meter-head assembly in series with the diode D1. Further, find the resistance $R_D$ and voltage drop $V_D$ of the diode D1 when the meter-head has a full scale display.

   Find the values of R14 through R17 so that they will indeed allow the meter-head to have a full scale display (with an average DC current of $I_m=50\;\mu A$ going through the meter-head), when the AC voltages of 10V, 50V, 250V and 1000V (RMS values) are applied to the corresponding scale positions.

4. DC current measurement

   The circuit shown in Figure 6 of the manual of the kit has some major mistake! Correct it.

   Find the values of R12 and R11 so that the meter-head will have a full scale display (with an current of $I_m=50\;\mu A$), when the DC currents of 2.5 mA and 25 mA are applied to the corresponding scale positions.

   Use the given values of R9=0.97 $\Omega$ and R10=0.04 $\Omega$ (not very accurate!), find current $I_m$ through the meter-head when the applied DC current is 10 A. For this current to be exactly $0.05\;mA$, what value should R10 take?

5. Resistance measurement (extra credits)

   First note that different from all measurements of voltage and current, where the meterhead receives input through R7, for resistance measurement, the input comes through R23, i.e., the meterhead assembly inside the dashed box used previously is no longer helpful. Now you need to analyze the circuit inside the box.

   • Before taking the measurement of a given external resistance $R$, the multimeter needs to be calibrated by adjusting R24 (assume the bottom part is x and the top part is 10-x), so that the meter-head shows a full scale display, when $R=0$ (with the two leads short circuited). Determine the value of this x.

   • Find the value of R19 for the scale of the $\times 1\;k\Omega$ resistance measurement, so that when an external resistance $R=20\;k\Omega$ being measured, the display of the meter is exactly halfway (in the middle), i.e., the current through the meter is $25\;\mu A$.