Network Theorems Notes for SSC JE Electrical Engineering

Network theorems are methods to solve electric circuits easily without using long calculations. They are the base of the Electrical Engineering paper in SSC JE, and every year questions come on Kirchhoff's laws, Thevenin's theorem, Norton's theorem and maximum power transfer. These network theorems notes for SSC JE explain every theorem in simple language with formulas, solved examples and practice questions.

Basic Laws

Series and Parallel Resistors

Superposition Theorem

• It is valid only for linear and bilateral circuits.
• The response in any element is the sum of the responses caused by each source acting alone.
• While one source works, the other voltage sources are replaced by a short circuit and the other current sources are replaced by an open circuit.
• It cannot be used for power, because power is not linear.

Thevenin's Theorem

• Any linear circuit can be replaced by a single voltage source Vth in series with a single resistance Rth.
• Vth is the open-circuit voltage across the load terminals.
• Rth is the resistance seen from the load terminals when all the independent sources are removed (voltage sources shorted and current sources opened).
• Load current IL = Vth / (Rth + RL).

Norton's Theorem

• Any linear circuit can be replaced by a current source IN in parallel with a resistance RN.
• IN is the short-circuit current through the load terminals.
• RN = Rth and Vth = IN × RN.
• Norton and Thevenin circuits are changed from one to another by source transformation.

Maximum Power Transfer Theorem

Example. A 12 V source with an internal resistance of 4 ohm feeds a load. For maximum power, the load must be 4 ohm, and the maximum power is 12² / (4 × 4) = 9 W.

Star-Delta Conversion

Example. Three equal delta resistors of 9 ohm each give a star with each arm = 9 × 9 / 27 = 3 ohm.

Other Theorems

Time Constants and Resonance

• Time constant of an RC circuit = RC, and of an RL circuit = L / R.
• Resonant frequency of a series RLC circuit f = 1 / (2π √LC).
• At series resonance, the impedance is minimum and equal to R, and the current is maximum.

Quick Tips

• Write the circuit again after removing the load before finding Vth and Rth.
• Remember that shorting a voltage source and opening a current source is the rule in both superposition and Thevenin.
• Check the maximum power condition with RL = Rth and the efficiency of 50 per cent.
• Practise the star-delta conversions, because they appear in many numericals.

Quick Revision Points

• KCL is based on conservation of charge and KVL on conservation of energy.
• Thevenin: Vth in series with Rth.
• Norton: IN in parallel with RN.
• Maximum power transfer occurs when RL = Rth.
• Superposition is valid only for linear and bilateral circuits.

Practice Questions With Answers

1. Which law is based on the conservation of charge?
   Answer: Kirchhoff's Current Law
2. In Thevenin's theorem, what is Vth?
   Answer: The open-circuit voltage across the load terminals
3. What is the condition for maximum power transfer?
   Answer: Load resistance equals source resistance
4. What is the efficiency at maximum power transfer?
   Answer: 50 per cent
5. Find the equivalent resistance of 6 ohm and 3 ohm in parallel.
   Answer: 2 ohm
6. What happens to a voltage source in the superposition theorem when it is not working?
   Answer: It is replaced by a short circuit
7. What is the Norton current IN?
   Answer: The short-circuit current through the load terminals
8. Three equal delta resistances of 12 ohm are converted into a star. Find each arm.
   Answer: 4 ohm
9. Is the superposition theorem valid for power?
   Answer: No
10. What is the time constant of an RL circuit?
    Answer: L / R

How to Practise This Chapter

Solve two network problems daily, one with Thevenin or Norton and one with KCL or KVL, and redraw the circuit at each step. Then solve questions from our practice papers and the previous year papers page. Read the next chapter, Transformer, and see all topics on the SSC JE Electrical Engineering notes page. For the electronics basics, read the Computer Knowledge notes.

Frequently Asked Questions

What are network theorems?

Network theorems are methods to simplify and solve electric circuits easily, such as Thevenin, Norton and superposition.

What is Kirchhoff's current law?

KCL says that the sum of the currents entering a node is equal to the sum of the currents leaving it.

What is Kirchhoff's voltage law?

KVL says that the algebraic sum of all the voltages around a closed loop is zero.

What is the superposition theorem?

It says that in a linear circuit the response is the sum of the responses produced by each source acting alone.

What is Thevenin's theorem?

It says that a linear circuit can be replaced by a voltage source in series with a resistance as seen from the load terminals.

What is Norton's theorem?

It says that a linear circuit can be replaced by a current source in parallel with a resistance as seen from the load terminals.

What is the maximum power transfer theorem?

It says that maximum power is delivered to the load when the load resistance is equal to the source (Thevenin) resistance.

What is the value of maximum power?

Maximum power is Vth squared divided by four times Rth.

How do I convert a delta into a star?

Each star resistance is the product of the two adjacent delta resistances divided by the sum of all the three delta resistances.

Which theorems are for linear circuits only?

Superposition, Thevenin and Norton theorems are applied to linear circuits.

Are network theorems important for SSC JE Electrical?

Yes. They are a basic topic, and the circuit questions are asked in every year.

How many questions come from network theory in SSC JE?

Usually four to six questions come from network theory and basic electrical concepts, but the number changes from year to year.