Lynn Gregory BIOE403 Lab 2

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Gregory Lynn & Eran Brown - 1Due 2/13//2014

BIOE 403

Instructor: Dr. Sal R. Riggio Jr., PhD, PE

Lab 2: Basic Electrical Circuits & Measurements

Purpose

The purpose of the first lab in BIOE 401 is to understand and utilize Kirchoffs laws in the interest of

solving circuits. Furthermore, the ability to design a resistor network with constraints and then analyze these circuits

is also a goal. Theoretical expectations for values based on these laws will be compared with measured values on a

protoboard circuit.

Materials

Agilent E3631A Triple Power SupplyAgilent 34401A Digital Multimeter1Proto board1Wire Jumper Kit (Various Wires)210 k W Resistors127 k W Resistor110 k PotentiometerMiscellaneous Resistors 1, 2, 8.2, 10, 15, & 27 k

Banana Clip WiresCoaxial cables

Procedure

Model the circuits in Fig. 1 and Fig. 2, and solve them for expressions of V1, V2, V3in terms of Vs, R1, R2, R3.


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Use a graphing data program (Excel) to plot each of the voltages (V1, V2, V3) found above as Vschanges

from 0 to 5 V in increments of 0.5 V. Also plot the currents (I1, I2, I3) as Vschanges from 0 to 5 V in increments

of 0.5 V. Create a data table for Expected & Actual measurements for Vs,V1, V2, V3, & % Error and label it Table

1. Create a data table for Expected & Actual measurements for I1, I2, I3, & % Error and label it Table 2.

Measure and record the true resistance value for all resistor materials, and label the 10k resistors to

differentiate from each other. Set the supply voltage to 5 V using the digital multimeter. Using 5 V for Vs, record

the expected values for V1, V2, V3computed earlier for the circuit of Figure 1 in Table 1. Do the same for I1, I2, I3

of the circuit in Figure 2 for Table 2. Ensuring that no power is supplied to the protoboard, construct the circuit in

Figure 1. Measure and record the actual voltages and record this data in Table 1. Compare these values with the

ones predicted and calculate the % Error in Table 1. Do the same for the circuit in Figure 2, recording values for I1,

I2, I3in Table 2, and then comparing these values using % Error.

Take the potentiometer and measure the resistance between the two outer terminals. While the multimeter

is still attached, use a screwdriver to rotate the knob and observe how the resistance changes. Move one probe to the

center terminal and repeat this procedure. With the power supply off, disassemble the previous circuit and assemble

the circuit displayed in Figure 4 above. Turn the knob on the potentiometer so that Vout= 1 V. With the power

off, remove the potentiometer carefully and measure the resistance (do not turn the knob!) between the upper/center

terminals and lower/center terminals.


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Observations Data Analysis

(1)

()

(2)

Table 1

R1 R2 R3 Vs

Expected () 10000 27000 10000 5 V

Actual () 9890 26930 98604.999

V

Expected Voltage (V) 1.0638 2.8723 1.0638

Actual Voltage(V) 1.058 2.882 1.055Error % 0.1065 0.0678 0.0867

Table 2

R1 R2 R3

Expected Current (mA) 0.2891 0.7813 0.2109

Actual Current (mA) 0.2918 0.078 0.2137

Error % 0.141 0.403 0.09

The Potentiometer

When the two outside leads were connected, turning the knob did nothing to affect the total resistance.

When one outside lead and the center lead were connected, the resistance varied between zero and Rtot

depending on the severity of the turn.

Vout= 0.9985 V when Rlower= 1910 and Rupper= 7442


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Design Problem

The brainstorming and work up to the final solution exists in the following pages, but the solution in a

simplified form is:

o Two Resistors in Parallel

8.2 k

10 k

Voltage Drop Measured across RLoad: % Error between 1.5 & Actual:

1.535 V 2.3653


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Conclusions

This lab successfully demonstrated the power and accuracy of KirchoffsVoltage and Current Laws and the

theoretical data was able to match expected values as an astonishingly good representation of realistic data. Error

percentages for both voltage and current were consistently below one percent, and some of this error likely arose due

to the assumption of ideal resistors during calculations. Many of these resistors actually varied a fraction or two of

its labelled value.

The potentiometer showed in practice what was suggested in theory. A potentiometer has three leads, the

upper and lower leads, which exist across the entire resistance of the pot, and a variable resistance lead, which falls

somewhere along the length of the interior resistor. When a voltage is applied to the upper and lower leads, turning

the screw had no effect since these two leads exist at opposite ends of the resistor at all times. When the same is

done to the middle lead and either end, turning the screw can vary the total resistance anywhere between 0 and R tot.

The design problem was solved through trial and guesswork displayed on the attached pages, but the

general strategy was to put a couple larger resisters in parallel in the hope to reduce the voltage to the desired

amount. The target resistance was calculated by assuming a resistor with resistance X could exist in a circuit with a

voltage drop of 1.5 across the load circuit. The target voltage was: 6.67k A voltage drop of 1.535 V was recorded

with the 8.2 and 10 k resistors in parallel, which corresponds to a 2.37% variation from the target voltage of 1.50

V. This design was certainly the most ideal possible since only two resistors were used and the total cost was $0.12,

far beneath the price point of $0.18. Since no one resistor was near enough to 6.67k, two resistors would be the

minimum required for success.

Lynn Gregory BIOE403 Lab 2

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