TF EIMLab1 Writeup

Kirchoff's Law (50 pnts)

Construct the circuit below

Enter the values of the DC voltage and Resisters that you used.

Use a voltmeter to measure the potential difference and resistances.

Variable	Measured Value
[math]V_A [/math]	20 Volts
[math]R_1[/math]	902 [math]\Omega[/math]
[math]R_2[/math]	10.2 [math]\Omega[/math]
[math]R_3[/math]	10.6 [math]\Omega[/math]

Enter the measured and predicted quantities in the table below

Given [math]V_A[/math] and the values of all resistors, use Kirchoff's laws to predict

a.) Predict the value of [math]V_B[/math]

[math]V_A - I_1R_1 = V_b [/math]

I_1 =?

Kirchoff's Loop theorem (Voltage Law)

[math]V_A -I_1(R_1+R_{tot}) = 0[/math] where R[math]_{tot}[/math] =resistance for [math]R_2[/math] and [math]R_3[/math] in series.

[math]R_{tot} = \frac{1}{\frac{1}{R_2} + \frac{1}{R_3}} = 5.2 \Omega[/math]

[math]I_1 = \frac{V_A}{R_1+R_{tot}} = \frac{ 20 \mbox{Volts}}{902 \Omega + 5.2 \Omega} = 22 \mbox{mA}[/math]

[math]V_b = V_A - I_1 R_1 = 20 - 0.022 \times 902 = 156[/math] mV

b.) Predict the values of the three currents.

[math]I_1 = I_2 + I_3[/math]

I[math]_2 R_2 - I_3 R_3 = 0[/math]

2 equations and 2 unkowns

[math]I_3 = \frac{I_1}{\frac{R_3}{R_2} +1} = \frac{22 mV}{\frac{10.6}{10.2}+1} = 10.8[/math] mA

[math]I_2 = I_1 - I_3 = 22 - 10.8 = 11.2[/math] mA

c.) compare your predictions and measurements by filling in the table below.

Variable	Measured Value	Predicted Value	% Difference
[math]V_B[/math]	103.5 mV	156	50%
[math]I_1[/math]	20.4 mA	22	7%
[math]I_2[/math]	9.5 mA	11.2	18%
[math]I_3[/math]	9.0 mA	10.8	20%

Internal resistance (30 pnts)

Measure the internal resistance of your power source by graphing the potential difference on the x-axis and the current on the y-axis for several values of the resistance [math]R_L[/math] shown in the circuit below. Begin with [math]R_L = 1k\Omega[/math] and then decrease it by a factor of 5 for each subsequent measurement. You can use a volt meter to measure the current and potential difference.

Questions (20 pnts)

1. What conservation law is involved in Kirchoff's Loop Theorem?
2. What does the slope in the internal resistance plot above represent?

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