Verification of Kirchhoff’s Voltage and Current laws

Experiment Number: 01

Aim of the Experiment: –

                     Verification of Kirchhoff’s Voltage Law (KVL) and Kirchhoff’s Current Law (KCL).

Apparatus Required: –

Sl. No.NameSpecificationQuantity
1Single Phase Auto Transformer ( Variac)5KVA, (0-270) V1 Nos.
2Voltmeter(0-250) V, MI1 Nos.
3Voltmeter(0-150) V, MI2 Nos.
4Ammeter(0-5) A, MI1 Nos.
5Ammeter(0-2) A, MI1 Nos.
6Connecting WirePVC Insulated CopperAs per Required
Table No. : 1.1

CIRCUIT DIAGRAM: –

Fig. No, 1.1

Theory: –

Kirchhoff’s Voltage Law-
It states that the algebraic sum of voltage drops in elements & voltage sources in any closed path (or mesh) in an electric network is equal to zero.

Fig. 1.2

Let us assuming the above fig.
By applying KVL in closed path (or loop )
V-IR1-IR2=0 or V=IR1+IR2

Kirchhoff’s Current Law –
It states that in any electrical circuit or network, the algebraic sum of currents meeting at any node (or junction or point) is equal to zero.

Fig. 1.3

Let us assume an electrical network as shown above.
‘A’ is the junction (or node) where all currents are meeting.
Assuming incoming current is +ve & outgoing currents are –ve at point ‘A’.
Then I-I1-I2=0 or I=I1+I2 or ΣI=0

Procedures: –

  1. All Instruments are connected as per circuit diagram shown in fig.
  2. The voltage is increased gradually by single phase auto- transformer & corresponding readings of Voltmeters & Ammeters are filled in observation table.

Precautions: –

  1. Don’t switch on power supply without concerning teacher.
  2. Single phase autotransformer must be kept at minimum potential point before switch on the experiment.

Observation Table: –

For KVL: –

Sl. No.V (in volts)V1 (in volts)V2 (in volts)V’=V1+V2 (in volts)%Error
={(V-V’)/V)*100}
1
2
3
4
5
6
7
8
Table No.: 1.2

For KCL: –

Sl. No.I (in Amps.)I1 (in Amps.)I2 (in Amps.)I’=I1+I2 (in Amps.)%Error
={(I-I’)/I)*100}
1
2
3
4
5
6
7
8
Table No.: 1.3

Conclusion:-


To be written by student.

Next

For Your Reference: –

Kirchhoff’s Voltage Law (KVL) and Kirchhoff’s Current Law (KCL) are fundamental principles in electrical engineering and circuit analysis.

  1. Kirchhoff’s Voltage Law (KVL): It states that the algebraic sum of the voltage drops (i.e., voltage across elements) in any closed loop of a circuit is equal to zero. This law is based on the principle of conservation of energy, stating that the total energy supplied to a closed loop must be equal to the total energy consumed. Mathematically, for a closed loop:
\[\sum_{n=1}^{N}V_n=0\]

Where 𝑉𝑛 is the voltage across the nth element in the loop and 𝑁 is the total number of elements in the loop.

2. Kirchhoff’s Current Law (KCL): It states that the algebraic sum of currents entering a node (or a closed boundary) in an electrical circuit is zero. This law is based on the principle of conservation of charge, stating that the total charge entering a node must equal the total charge leaving it.

Mathematically, for a node:

\[\sum_{n=1}^{N} I_N=0\] \[Where \;𝐼_n \;is\; the \;current\; entering\; (𝐼_n>0)\; or\; leaving \;(I_n<0)\; the\; node,\] \[and\;𝑁\;is\; the\; total\; number\; of\; currents\; at\; the\; node.\]

Verification of these laws involves applying them to different circuits and analyzing whether they hold true. It’s important to ensure that the assumptions and conventions used in circuit analysis, such as sign conventions for voltage and current, are consistent with the application of these laws.

Some Viva-voce questions:

  1. What is Kirchhoff’s Voltage Law (KVL), and why is it important in circuit analysis?
    • KVL states that the sum of voltages around any closed loop in a circuit is zero. It’s important because it’s based on the conservation of energy principle and provides a systematic method for analyzing complex circuits.
  2. Can you explain how Kirchhoff’s Voltage Law is applied in circuit analysis?
    • In circuit analysis, KVL is applied by traversing a closed loop in a circuit and summing up the voltage drops across all elements (resistors, capacitors, and inductors) encountered in the loop. The algebraic sum of these voltage drops must equal zero.
  3. What are the assumptions made when applying Kirchhoff’s Voltage Law?
    • The assumptions include the ideal behavior of circuit elements (like resistors having linear voltage-current characteristics), no significant electromagnetic interference, and steady-state conditions unless stated otherwise.
  4. Explain Kirchhoff’s Current Law (KCL) and its significance.
    • KCL states that the algebraic sum of currents at any node (or junction) in a circuit is zero, based on the conservation of charge principle. It’s crucial for analyzing current distribution in complex circuits and ensures that the current entering a node equals the current leaving it.
  5. How is Kirchhoff’s Current Law applied practically in circuit analysis?
    • In circuit analysis, KCL is applied by summing up currents at each node, ensuring that the sum equals zero. This involves assigning currents entering the node as positive and currents leaving as negative, following a sign convention.
  6. What happens if Kirchhoff’s Voltage Law or Kirchhoff’s Current Law seems to be violated in a circuit analysis?
    • If these laws appear to be violated, it usually indicates errors in circuit analysis, such as incorrect application of the laws, incorrect assumptions about circuit behavior, or faulty measurements. Revisiting the analysis and ensuring all conditions are met typically resolves such discrepancies.
  7. Can you give an example of a circuit problem where you would apply both KVL and KCL?
    • An example could be analyzing a circuit with multiple loops and nodes, such as a series-parallel circuit with resistors. Applying KVL to each loop and KCL to each node would help determine the currents and voltages across different elements in the circuit.(Explain with Circuit Diagram)