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
$V_A$	20 Volts
$R_1$	902 $\Omega$
$R_2$	10.2 $\Omega$
$R_3$	10.6 $\Omega$

Enter the measured and predicted quantities in the table below

Given $V_A$ and the values of all resistors, use Kirchoff's laws to predict

a.) Predict the value of $V_B$

$V_A - I_1R_1 = V_b$

I_1 =?

Kirchoff's Loop theorem (Voltage Law)

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

$R_{tot} = \frac{1}{\frac{1}{R_2} + \frac{1}{R_3}} = 5.2 \Omega$

$I_1 = \frac{V_A}{R_1+R_{tot}} = \frac{ 20 \mbox{Volts}}{902 \Omega + 5.2 \Omega} = 22 \mbox{mA}$

$V_b = V_A - I_1 R_1 = 20 - 0.022 \times 902 = 156$ mV

b.) Predict the values of the three currents.

$I_1 = I_2 + I_3$

I$_2 R_2 - I_3 R_3 = 0$

2 equations and 2 unkowns

$I_3 = \frac{I_1}{\frac{R_3}{R_2} +1} = \frac{22 mV}{\frac{10.6}{10.2}+1} = 10.8$ mA

$I_2 = I_1 - I_3 = 22 - 10.8 = 11.2$ mA

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

Variable	Measured Value	Predicted Value	% Difference
$V_B$	103.5 +/- 50 mV	156	50%
$I_1$	20.4 mA	22	7%
$I_2$	9.5 mA	11.2	18%
$I_3$	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 $R_L$ shown in the circuit below. Begin with $R_L = 1k\Omega$ 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_{Load} ($\Omega$)	V (Volts)	I (mA)
10	1.42 $\pm$ 0.06	118 $\pm$ 3
93	1.55$\pm$ 0.01	16.15 $\pm$ 0.05
990	1.575 $\pm$ 0.005	1.54 $\pm$ 0.04
10110	1.579 $\pm$ 0.005	0.146 $\pm$ 0.005
15060	1.579 $\pm$ 0.005	0.101 $\pm$ 0.003

Below I set R= 95 $\Omega$ 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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