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Verification of Kirchhoff's Laws Using Multimeter and Breadboard

Kirchhoff's Current Law (KCL / Junction Rule) and Kirchhoff's Voltage Law (KVL / Loop Rule) using a digital multimeter and a breadboard circuit.

Physics Experiments 20 September, 2026 10 min read

Verification of Kirchhoff's Laws Using Multimeter and Breadboard

Physics Lab Experiment • DC Circuits • Kirchhoff's Current Law & Voltage Law
Aim

To verify Kirchhoff's Current Law (KCL / Junction Rule) and Kirchhoff's Voltage Law (KVL / Loop Rule) using a digital multimeter and a breadboard circuit with known resistors and a DC power supply.

Apparatus Required

1 Digital Multimeter (DMM)
2 Breadboard (830-point or similar)
3 Resistor R1 = 100 Ω (¼ W)
4 Resistor R2 = 220 Ω (¼ W)
5 Resistor R3 = 330 Ω (¼ W)
6 DC Power Supply (5 V regulated)
7 Connecting / Jumper Wires
8 9 V Battery with Clip (optional source)

Theory & Principle

Gustav Kirchhoff formulated two fundamental laws in 1845 that govern the behaviour of currents and voltages in electrical circuits. These laws are the foundation for analysing any circuit, no matter how complex, and are direct consequences of two conservation principles from physics.

Kirchhoff's Current Law (KCL) — The Junction Rule

KCL states that the algebraic sum of all currents at any junction (node) in a circuit is zero. In practical terms, the total current flowing into a junction equals the total current flowing out of that junction. No charge accumulates at a node in a steady-state circuit.

This law is a direct consequence of the conservation of electric charge. Since charge is neither created nor destroyed at a junction, every coulomb that arrives must also depart.

Σ Ientering = Σ Ileaving    or equivalently    Σ I = 0  (at any junction)

For example, if three branches meet at junction A carrying currents I1, I2, and I3, and I1 flows into the junction while I2 and I3 flow out, then: I1 = I2 + I3.

Kirchhoff's Voltage Law (KVL) — The Loop Rule

KVL states that the algebraic sum of all potential differences (voltages) around any closed loop in a circuit is zero. When you traverse a complete loop, the energy gained per unit charge from EMF sources exactly equals the energy lost per unit charge across resistances.

This law follows from the conservation of energy. A charge that completes a closed path returns to the same electric potential it started from, so the net energy change must be zero.

Σ V = 0  (around any closed loop)    or    Σ EMF = Σ IR  (drops)

For a loop containing a battery of EMF E and resistors R1, R2 carrying current I, KVL gives: E − IR1 − IR2 = 0.

Summary of Both Laws

Kirchhoff's Current Law (KCL): At any junction, the sum of currents entering equals the sum of currents leaving. Mathematically: ΣI = 0. Basis: Conservation of charge.

Kirchhoff's Voltage Law (KVL): Around any closed loop, the sum of all EMFs equals the sum of all IR voltage drops. Mathematically: ΣV = 0. Basis: Conservation of energy.

How We Verify These Laws Experimentally

We construct a circuit with multiple branches meeting at identifiable junctions. Using a digital multimeter:

  • To verify KCL: We measure the current in the main line (entering a junction) and in each branch (leaving the junction). If the entering current equals the sum of the leaving branch currents within experimental error, KCL is verified.
  • To verify KVL: We measure the voltage drop across every component in a closed loop (each resistor and the source). If the algebraic sum of these voltages around the loop equals zero (within experimental error), KVL is verified.
Why a breadboard? A breadboard allows rapid, solderless prototyping. Components and wires are inserted into spring-clip rows, making it easy to build, modify, and test circuits without permanent connections. The internal bus structure connects rows of five holes, providing convenient junction points for measuring KCL.

Circuit Diagram

R₁=100Ω R₂=220Ω R₃=330Ω + − E=5V A B C D I I₁ I₂ Loop 1 Loop 2 Loop 1: E → R₁ → R₂ → back to E Loop 2: E → R₃ → back to E At A: I = I₁ + I₂

Figure: Circuit with DC source (5V), two parallel branches. Branch 1 has R1 (100Ω) and R2 (220Ω) in series; Branch 2 has R3 (330Ω). Junctions A, B, C are marked. I is the total current; I1 flows through Branch 1; I2 flows through Branch 2.

Procedure

Part A — Verification of Kirchhoff's Current Law (KCL)

  1. Build the circuit on the breadboard as shown in the circuit diagram. Insert R1 (100Ω) and R2 (220Ω) in series across two rows to form Branch 1. Insert R3 (330Ω) across two separate rows to form Branch 2. Connect both branches in parallel between the common junctions A and B using jumper wires.
  2. Connect the DC supply. Attach the positive terminal of the 5V DC power supply to junction A and the negative terminal to junction C (which connects to junction B through the return path). Switch on the supply.
  3. Measure the total current (I). Set the digital multimeter to the DC current (mA) range. Break the main line between the positive terminal of the supply and junction A. Insert the multimeter in series at this break. Record the total current I entering junction A.
  4. Measure Branch 1 current (I1). Disconnect the multimeter from the main line and reconnect that wire. Now break Branch 1 (between A and R1) and insert the multimeter in series. Record I1, the current through Branch 1 (R1–R2 path).
  5. Measure Branch 2 current (I2). Similarly, break Branch 2 (between A and R3) and insert the multimeter in series. Record I2, the current through Branch 2 (R3 path).
  6. Verify KCL. Compute I1 + I2 and compare it with the measured I. If I ≈ I1 + I2 within experimental uncertainty, KCL is verified at junction A. Repeat for at least two more sets of readings (by slightly adjusting the supply voltage, if variable) to improve confidence.

Part B — Verification of Kirchhoff's Voltage Law (KVL)

  1. Keep the same circuit connected with the 5V DC supply active. Set the digital multimeter to the DC voltage (V) range.
  2. Measure the supply voltage (Vsource). Place the multimeter probes across the DC power supply terminals. Record Vsource.
  3. Measure voltage across R1 (VR1). Place the multimeter probes across R1 (the 100Ω resistor). Record the voltage drop VR1.
  4. Measure voltage across R2 (VR2). Place the probes across R2 (the 220Ω resistor). Record VR2.
  5. Measure voltage across R3 (VR3). Place the probes across R3 (the 330Ω resistor). Record VR3.
  6. Verify KVL. For Loop 1 (E → R1 → R2): check that Vsource − VR1 − VR2 ≈ 0. For Loop 2 (E → R3): check that Vsource − VR3 ≈ 0. If both sums are approximately zero, KVL is verified.
Precautions:
  • Always connect the multimeter in series for current measurement and in parallel for voltage measurement. Reversing this can damage the meter or blow its fuse.
  • Ensure all breadboard connections are firm. Loose connections cause erratic readings and do not represent the intended circuit.
  • Start with the highest current range on the multimeter and step down. This protects the meter from overcurrent damage.
  • Switch off the power supply before changing the multimeter position in the circuit to avoid short circuits.
  • Check resistor values with the multimeter (in resistance mode) before inserting them, as the actual resistance may deviate from the colour-code value due to manufacturing tolerance (±5% or ±10%).

Observation Table

Table A — Verification of KCL (Junction Rule)

Supply voltage kept at 5.00 V for all readings. Currents measured in mA.

Obs. No. Junction Iin (mA) I1 out (mA) I2 out (mA) I1+I2 (mA) ΣI = Iin−(I1+I2) (mA)
1 A 30.6 15.5 14.9 30.4 +0.2
2 A 30.8 15.6 15.1 30.7 +0.1
3 A 30.5 15.4 15.0 30.4 +0.1

ΣI &approx; 0 in all cases, verifying KCL. Small residuals (< 0.7%) are within multimeter accuracy limits.

Table B — Verification of KVL (Loop Rule)

Voltages measured in volts (V) with the circuit carrying its natural current.

Loop Vsource (V) VR1 (V) VR2 (V) VR3 (V) ΣV (V)
Loop 1 (E, R1, R2) 5.00 1.55 3.42 — 5.00 − 1.55 − 3.42 = +0.03
Loop 2 (E, R3) 5.00 — — 4.97 5.00 − 4.97 = +0.03

ΣV &approx; 0 for both loops, verifying KVL. Residuals of 0.03 V (<1%) are well within acceptable experimental error.

Calculations

Expected (Theoretical) Values

We first compute the expected currents using Ohm's law and the known resistor values.

Branch 1: R1 + R2 = 100 + 220 = 320 Ω
I1 = V / (R1 + R2) = 5.00 / 320 = 15.63 mA

Branch 2: R3 = 330 Ω
I2 = V / R3 = 5.00 / 330 = 15.15 mA

Total current: I = I1 + I2 = 15.63 + 15.15 = 30.78 mA

Equivalent resistance:
1/Req = 1/320 + 1/330 = (330 + 320) / (320 × 330) = 650 / 105600
Req = 105600 / 650 = 162.46 Ω
Check: I = 5.00 / 162.46 = 30.78 mA ✓

Expected Voltage Drops

VR1 = I1 × R1 = 15.63 × 10−3 × 100 = 1.563 V
VR2 = I1 × R2 = 15.63 × 10−3 × 220 = 3.438 V
VR3 = I2 × R3 = 15.15 × 10−3 × 330 = 5.000 V

KVL Verification (Theoretical)

Loop 1: E − VR1 − VR2 = 5.000 − 1.563 − 3.438 = 0.000 V   ✓

Loop 2: E − VR3 = 5.000 − 5.000 = 0.000 V   ✓

Comparison with Measured Values

KCL at junction A (Reading 1):
Measured: I = 30.6 mA,   I1 + I2 = 15.5 + 14.9 = 30.4 mA
Discrepancy = 30.6 − 30.4 = 0.2 mA
Percentage error = (0.2 / 30.6) × 100 = 0.65%

KVL Loop 1 (Measured):
ΣV = 5.00 − 1.55 − 3.42 = 0.03 V
Percentage error = (0.03 / 5.00) × 100 = 0.60%

KVL Loop 2 (Measured):
ΣV = 5.00 − 4.97 = 0.03 V
Percentage error = (0.03 / 5.00) × 100 = 0.60%

All measured values agree with theoretical predictions within 1%, which is well within the ±2–3% range expected from typical instrument and component tolerances.

Result

Both Kirchhoff's laws are verified experimentally:

KCL: At junction A, the current entering (I) was found to be equal to the sum of currents leaving (I1 + I2) within an experimental error of less than 1%.

KVL: For both closed loops, the algebraic sum of voltages was found to be approximately zero (ΣV &approx; 0), with a deviation of less than 1%.

The small discrepancies (0.6–0.7%) are attributable to multimeter accuracy, contact resistance, and resistor tolerance. Both laws hold true within the expected experimental uncertainty of ±2–3%.

Sources of Error

  1. Multimeter accuracy and resolution: A typical digital multimeter has an accuracy of ±0.5–1% of reading plus a few least-significant digits. This introduces a systematic uncertainty in every current and voltage measurement, which propagates into the KCL and KVL sums.
  2. Resistance of connecting wires: Jumper wires and breadboard internal traces have small but nonzero resistance (typically 0.1–0.5 Ω per connection). These unaccounted voltage drops cause the measured voltage across a resistor to be slightly less than the actual drop, leading to a nonzero KVL sum.
  3. Contact resistance at breadboard connections: The spring-clip contacts inside a breadboard introduce variable contact resistance, especially if the component leads are thin or oxidised. This adds unpredictable voltage drops and can slightly alter branch currents.
  4. Resistor tolerance: Standard carbon-film resistors have a tolerance of ±5% (gold band) or ±10% (silver band). The actual resistance may differ from the marked value, causing measured currents and voltages to deviate from values calculated using nominal resistances.
  5. Temperature effects: As current flows through resistors, they dissipate power and heat up. The resistance of most materials increases with temperature (positive temperature coefficient), which causes a gradual drift in current and voltage readings over time, especially in high-precision measurements.

Viva Voce Questions

State and explain Kirchhoff's Current Law (KCL).
Kirchhoff's Current Law states that the algebraic sum of all currents meeting at any junction (node) in an electrical circuit is zero. If we assign positive signs to currents entering a junction and negative signs to currents leaving, then ΣI = 0. Physically, this means the total current flowing into a junction equals the total current flowing out. For example, if a junction has currents I1 entering and I2, I3 leaving, then I1 = I2 + I3. This law is a statement of the conservation of electric charge: since charge cannot accumulate at a point in a steady-state circuit, all charge that arrives must depart.
State and explain Kirchhoff's Voltage Law (KVL).
Kirchhoff's Voltage Law states that the algebraic sum of all the electromotive forces (EMFs) and voltage drops (IR products) around any closed loop in a circuit is zero: ΣV = 0. When traversing a loop, we add EMFs that push current in the direction of traversal and subtract those opposing it; similarly, we subtract IR drops in the direction of current and add them when going against the current. This law is a consequence of the conservation of energy: a unit positive charge traversing a complete closed path returns to its starting potential, so the net energy gained (from EMFs) must exactly equal the net energy lost (as IR drops).
What is the physical basis of each of Kirchhoff's laws?
KCL is based on the conservation of electric charge. In a steady-state circuit, charge does not accumulate at any point. Every electron that arrives at a junction must leave through one of the connected branches. Therefore, the net current at any node must be zero. KVL is based on the conservation of energy. The electric potential is a single-valued function of position. When a charge completes a full loop and returns to its starting point, it is at the same potential, so the total work done on it (by EMF sources) must equal the total work done by it (through resistive drops). Hence the algebraic sum of all potential changes around a loop is zero.
What are the sign conventions used while applying Kirchhoff's laws?
For KCL: Currents entering a junction are taken as positive, and currents leaving are taken as negative (or vice versa, as long as the convention is consistent). The sum must then equal zero. For KVL: Choose a direction to traverse the loop (clockwise or counter-clockwise). When moving through an EMF source from − to + terminal, the EMF is positive (voltage rise); from + to −, it is negative (voltage drop). When moving through a resistor in the direction of current flow, the voltage change is −IR (a drop); against the current, it is +IR (a rise). These conventions ensure the algebraic sum correctly yields zero for a valid circuit loop.
How are Kirchhoff's laws used to derive the Wheatstone Bridge balance condition?
A Wheatstone Bridge consists of four resistances P, Q, R, S arranged in a diamond, with a galvanometer (G) connected between the two midpoints and a battery across the two endpoints. At balance, no current flows through the galvanometer (IG = 0). Applying KCL at the junctions: the current through P equals the current through Q (since none diverts through G), and the current through R equals the current through S. Applying KVL to the loop containing P, G, and R: IP·P − IG·G − IR·R = 0. Since IG = 0, this gives IP·P = IR·R. Similarly, from the loop containing Q, G, and S: IQ·Q = IS·S. Dividing these two equations and using the KCL conditions (IP = IQ and IR = IS), we get the balance condition: P/Q = R/S.
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