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]\displaystyle{ V_A }[/math]	20 Volts
[math]\displaystyle{ R_1 }[/math]	902 [math]\displaystyle{ \Omega }[/math]
[math]\displaystyle{ R_2 }[/math]	10.2 [math]\displaystyle{ \Omega }[/math]
[math]\displaystyle{ R_3 }[/math]	10.6 [math]\displaystyle{ \Omega }[/math]

Enter the measured and predicted quantities in the table below

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

a.) Predict the value of [math]\displaystyle{ V_B }[/math]

[math]\displaystyle{ V_A - I_1R_1 = V_b }[/math]

I_1 =?

Kirchoff's Loop theorem (Voltage Law)

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

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

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

[math]\displaystyle{ 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]\displaystyle{ I_1 = I_2 + I_3 }[/math]

I[math]\displaystyle{ _2 R_2 - I_3 R_3 = 0 }[/math]

2 equations and 2 unkowns

[math]\displaystyle{ 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]\displaystyle{ 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]\displaystyle{ V_B }[/math]	103.5 mV	156	50%
[math]\displaystyle{ I_1 }[/math]	20.4 mA	22	7%
[math]\displaystyle{ I_2 }[/math]	9.5 mA	11.2	18%
[math]\displaystyle{ 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]\displaystyle{ R_L }[/math] shown in the circuit below. Begin with [math]\displaystyle{ 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.

R ([math]\displaystyle{ \Omega }[/math])	V (mv)	I (mA)

Below I set R= 95 [math]\displaystyle{ \Omega }[/math] and changed V

V (mv)	I (mA)
126.1	0.79
300	2.64
500	4.62
1000	9.29
2000	18.78
3000	30.4

Now lets try to fix V and change R

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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