Lab 2

ENSC 220 – Lab 2:

Authors: Tyler Lee · Kian Bellinger · Kavahn Ahluwalia
Bench #2

The circuit under test consists of:

• $(R_1)$in series between the supply rail at node A and node B.
• ($R_2$) and ($R_3$) connected in parallel between node B and ground.

With an applied supply voltage $(V_{\text{s}}\approx 5V)$, Kirchhoff’s laws give:

$$V_{\text{s}}=V_{AB}+V_B$$ $$I_1=I_2+I_3$$

where:

$$I_1=\frac{V_{\text{s}}}{R_1+R_{23}},I_2=\frac{V_B}{R_2},I_3=\frac{V_B}{R_3},R_{23}=\frac{R_2{R}_3}{R_2+R_3}$$

Results

Measured Component Values

Component	Measured (kΩ)	Nominal (kΩ)	Error (%)
R1	0.46494	0.470	0.48
R2	2.1652	2.20	1.58
R3	1.1895	1.20	0.88

Equivalent resistance of $R_2\Vert R_3$:

$$R_{23}=0.768\text{kΩ}$$

Total series resistance:

$$R_{\text{eq}}=R_1+R_{23}=1.233\text{kΩ}$$

Voltage Measurements

Quantity	Value (V)	DMM spec (%)
(V_A)	5.033	0.06
(V_B)	3.134	0.08
(V_{AB})	1.8984	0.12

Current Measurements

Branch	Value (mA)	DMM spec (%)
(I_1)	4.045	0.12
(I_2)	1.442	0.26
(I_3)	2.617	0.16

Kirchhoff Verification

KVL

$$V_A\stackrel{?}{=}{V}_{AB}+V_B$$

	(V_A) (V)	(V_{AB}+V_B) (V)	Error (%)
Measured	5.033	5.0324	0.012

KCL

$$I_1\stackrel{?}{=}{I}_2+I_3$$

	(I_1) (mA)	(I_2+I_3) (mA)	Error (%)
Measured	4.045	4.059	−0.35

Comparison with Theory

Using measured resistances:

$$I_1^{(\text{th})}=\frac{V_A}{R_{\text{eq}}}=4.083\text{mA}$$ $$V_{AB}^{(\text{th})}=I_1^{(\text{th})}{R}_1=1.8984\text{V}$$ $$V_B^{(\text{th})}=V_A-V_{AB}^{(\text{th})}=3.1346\text{V}$$

Corresponding branch currents:

$$I_2^{(\text{th})}=1.448\text{mA},I_3^{(\text{th})}=2.635\text{mA}$$

Quantity	Measured	Theory	% Diff
(I_1) (mA)	4.045	4.083	−0.93
(V_{AB}) (V)	1.8984	1.8984	0.00
(V_B) (V)	3.134	3.135	−0.02
(I_2) (mA)	1.442	1.448	−0.40
(I_3) (mA)	2.617	2.635	−0.69

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Discussion

• KVL: Error of 0.012 % is an order of magnitude smaller than the DMM’s 0.06 % voltage accuracy.
• KCL: Error of 0.35 % is smaller than the combined current-measurement uncertainties.
• Deviations are from resistor tolerances, impedance of the DMM when measuring voltage (≈10 MΩ), and small supply-voltage drift from high impedance wires.

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Conclusion

Both Kirchhoff’s laws have been experimentally validated for a simple resistive network. All observed discrepancies are significantly smaller than the specified accuracy of the measuring instrumentation, confirming that the experimental procedure and uncertainty analysis are sound.