Lab Practical

Practical 2

ECE279 6 min read 7 practicals total

Practical 2: KVL Voltage Hunt

1. Aim/Objective

To verify Kirchhoff's Voltage Law (KVL) in a DC resistive network by measuring voltage drops across various components in closed loops and comparing the algebraic sum with theoretical predictions.

2. Apparatus/Components Required

S.No	Component/Equipment	Specification	Quantity
1	DC Regulated Power Supply (RPS)	0-30V, 1A (Dual Channel preferred)	1
2	Digital Multimeter (DMM)	Standard Laboratory Grade	1
3	Breadboard	Standard size	1
4	Resistors (Fixed)	$1k\Omega$ , $2.2k\Omega$ , $3.3k\Omega$ (1/4 Watt)	1 each
5	Connecting Wires	Single strand hook-up wires	As req.

3. Theory

Kirchhoff's Voltage Law (KVL) states that the algebraic sum of all voltages around any closed loop (mesh) in a circuit is equal to zero. This is a manifestation of the Law of Conservation of Energy.

Mathematically:

\sum_{k=1}^{n} V_k = 0

Sign Convention for Analysis:

Voltage Rise: Moving from negative (-) to positive (+) terminal (e.g., traversing a battery from - to +). Value is taken as Positive.
Voltage Drop: Moving from positive (+) to negative (-) terminal (e.g., current flowing through a resistor). Value is taken as Negative.

In a practical "Voltage Hunt," we measure the potential difference across every component. If we traverse a loop and sum these values (respecting polarity), the result should ideally be zero.

A theoretical diagram explaining KVL Sign Convention. The image should show a simple circuit loop wi... — AI-generated image — may contain inaccuracies

4. Circuit Diagram / Setup

We will utilize a T-Network circuit which provides two distinct meshes for analysis.

Circuit Components:

V1: 10V DC Source
R1: $1k\Omega$ (Series arm)
R2: $2.2k\Omega$ (Shunt/Shared arm)
R3: $3.3k\Omega$ (Output arm)

A clean, standard schematic diagram of a T-network circuit for KVL verification. Show a DC Voltage S... — AI-generated image — may contain inaccuracies

A realistic breadboard wiring diagram corresponding to the T-network schematic above. Show a white b... — AI-generated image — may contain inaccuracies

5. Procedure

Preparation: Check the resistance values of $R_1$ , $R_2$ , and $R_3$ using the Digital Multimeter (Ohmmeter mode) and record the actual measured values.
Circuit Assembly: Connect the circuit on the breadboard as shown in the breadboard layout diagram. Ensure all connections are tight.
Power Up: Switch on the Regulated Power Supply (RPS) and set the output voltage ( $V_s$ ) to exactly 10V.
Measurement Strategy: You will measure voltage drops across every element. Crucial: Always place the Red Probe of the DMM at the point where current enters the component and the Black Probe where current leaves to get a positive reading for a drop.
Measure Loop 1 (Mesh 1):
- Measure voltage across Source ( $V_s$ ).
- Measure voltage across $R_1$ ( $V_{R1}$ ).
- Measure voltage across $R_2$ ( $V_{R2}$ ).
Measure Loop 2 (Mesh 2):
- Measure voltage across $R_2$ ( $V_{R2}$ ). Note: This is the shared branch.
- Measure voltage across $R_3$ ( $V_{R3}$ ).
Verification: Record all readings with proper signs in the observation table.

A close-up illustration of a Digital Multimeter (DMM) measuring voltage across a resistor on a bread... — AI-generated image — may contain inaccuracies

6. Observations & Readings

Input Voltage ( $V_s$ ): ___ V (Set to approx 10V)

Resistor Values (Measured):

$R_1$ : ____ $\Omega$
$R_2$ : ____ $\Omega$
$R_3$ : ____ $\Omega$

Table 1: Voltage Drops

Component	Theoretical Voltage (V)	Practical (Measured) Voltage (V)
$V_{R1}$	Calculate in Section 7
$V_{R2}$	Calculate in Section 7
$V_{R3}$	Calculate in Section 7

Table 2: KVL Verification (Algebraic Sum)

Loop Path	Equation	Calculation (Sum of Measured Values)	Result
Mesh 1	$V_s - V_{R1} - V_{R2}$	$10 - (\dots) - (\dots)$	_____ V
Mesh 2	$V_{R2} - V_{R3}$	$(\dots) - (\dots)$	_____ V
Outer Loop	$V_s - V_{R1} - V_{R3}$	$10 - (\dots) - (\dots)$	_____ V

Note: In Mesh 2, if taking clockwise direction, we go "up" against the current in R2 (Rise) and "down" with current in R3 (Drop). So equation is $V_{R2} - V_{R3} = 0$ .

A visualization of the loops for the observation table equations. Show the circuit again with three ... — AI-generated image — may contain inaccuracies

7. Calculations

Step 1: Calculate Total Resistance ( $R_{eq}$ )
$R_2$ and $R_3$ are in parallel (since $R_3$ goes to ground and $R_2$ goes to ground in this T-config, effectively parallel connected to node after $R_1$ ).

R_p = \frac{R_2 \times R_3}{R_2 + R_3} = \frac{2200 \times 3300}{2200 + 3300} = 1320 \Omega

R_{total} = R_1 + R_p = 1000 + 1320 = 2320 \Omega

Step 2: Calculate Total Current ( $I_{total}$ )

I_{total} = \frac{V_s}{R_{total}} = \frac{10V}{2320\Omega} \approx 4.31 mA

Step 3: Theoretical Voltage Drops

$V_{R1} = I_{total} \times R_1 = 4.31 mA \times 1k\Omega = \textbf{4.31 V}$
Voltage at Node A ( $V_A$ ) = $V_s - V_{R1} = 10 - 4.31 = 5.69 V$
Since and are in parallel connected to Node A:
- $V_{R2} = \textbf{5.69 V}$
- $V_{R3} = \textbf{5.69 V}$

Step 4: % Error Calculation

\% Error = \frac{\text{Theoretical} - \text{Practical}}{\text{Theoretical}} \times 100

A graphical representation of the calculation flow (Block Diagram style). Block 1: "Measure Resistor... — AI-generated image — may contain inaccuracies

8. Result

The Kirchhoff’s Voltage Law (KVL) has been verified for the given resistive network.

Mesh 1 Sum: The algebraic sum of voltages in Mesh 1 was found to be ______ V (approx 0V).
Mesh 2 Sum: The algebraic sum of voltages in Mesh 2 was found to be ______ V (approx 0V).

Small deviations from zero are attributed to tolerance of resistors, contact resistance of the breadboard, and internal resistance of the multimeter.

9. Viva Questions

Q: On what fundamental principle is KVL based?
- A: KVL is based on the Law of Conservation of Energy. It states that energy gained by charge in a source must be dissipated across passive elements in a closed loop.
Q: Why must the DMM be connected in parallel to measure voltage?
- A: Voltage is a potential difference between two points. Connecting in parallel allows the meter to sample the energy difference across the component without interrupting the circuit path. Ideally, a voltmeter has infinite resistance.
Q: If you traverse a resistor opposite to the direction of current, is it a voltage rise or drop?
- A: It is considered a Voltage Rise (+), because you are moving from a lower potential to a higher potential.
Q: Can KVL be applied to an open loop?
- A: No, KVL specifically applies to closed conducting paths (loops or meshes) where the starting and ending point are the same.
Q: What happens if you sum the voltages but get a value significantly non-zero (e.g., 2V)?
- A: This indicates an error: loose connections, a faulty component, incorrect measurement polarity, or a battery that is draining under load.

A "Troubleshooting" infographic. Split into two panels. Panel A: "Correct KVL" showing a balanced sc... — AI-generated image — may contain inaccuracies

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