**Q. 1. What is an electric network?**

**Ans.** An electric network is an interconnection of physical electrical devices such as an energy source (or sources), an energy converter or converters (load or loads), and conductors that connect them.

**Q. 2. What is an energy source?**

**Ans.** An energy source (or source), such as primary or secondary cell, a generator, and the like, is a device that converts chemical, mechanical, thermal or some other form of energy into the electrical energy.

**Q. 3. What is an energy converter?**

**Ans.** An energy converter, also called the load, such as lamp, heating appliance, or electric motor, converts electrical energy into light, heat, mechanical work etc.

**Q. 4. What is meant by ‘node’?**

**Ans.** A junction or node is a point in a network where two or more branches meet.

**Q. 5. Distinguish between mesh and loop of network.**

**Ans.** A loop is a closed path in a network formed by a number of connected branches. Mesh is a loop that contains no other loop within it.

**Q. 6. What is the utility of superposition theorem?**

**Ans.** This theorem is applied when we are to determine the current in one particular branch of a network containing several voltage sources or current sources or both voltage sources and current sources.

**Q. 7. What is the utility of Thevenin theorem?**

**Ans.** Thevenin’s theorem is advantageous when we are to determine the current in a particular element of a linear bilateral network particularly when it is desired to find the current which flows through a resistor for its different values. It makes the solution of the complicated networks (particularly electronic networks) quite simple.

**Q. 8. What is maximum power transfer theorem?**

**Ans.** A resistive load, served through a resistive network, will abstract maximum power when the load resistance value is the same as the resistance ‘viewed by the load as it looks back into the network’.

**Q. 9. Where does the Millman theorem find utility?**

**Ans.** In practice, cases frequently arise where a network has only two terminal points between which any number of parallel branches may be connected. Their calculations can be greatly simplified by the use of Millman’s theorem, which is combination of Thevenin’s and Norton’s theorem. This theorem enables a number of voltage (or current) sources to be combined into a single voltage (or current) source.

**Q. 10. Give the relationship between resistances connected in delta and equivalent star systems?**

**Ans.** The equivalent star resistance connected to a given terminal is equal to the product of the two delta resistances connected to the same terminal divided by the sum of the delta connected resistances.

**Q. 11. Give the relationship between resistances connected in star and equivalent delta systems?**

**Ans.** The equivalent delta resistance between two terminals is the sum of the two star resistances connected to those terminals plus the product of the same divided by the third star resistance.

**Q. 12. What is Tellegen’s theorem and what is its utility?**

**Ans.** According to this theorem the summation of instantaneous powers for the n-branches in an electric network is always zero. Alternatively this theorem may be narrated as below :

If there are n elements in any network; i_{1}, i_{2}, i_{3}……..i_{n} are the respective instantaneous currents flowing through these elements satisfying Kirchhoff’s current law and v_{1}, v_{2}, v_{3},……v_{n }are the respective instantaneous voltages across these elements satisfying Kirchhoff’s voltage law, then

where v_{k} is the instantaneous voltage across k_{th} element and i_{k} is the instantaneous current flowing through this element.

This theorem is applicable to a very general class of lumped networks composed of elements that are linear or non-linear, active or passive, time invariant or time variant.

**Q. 13. Explain, why bending a wire does not affect electrical resistance?**

**Ans.** Free electrons in a wire have small value of drift velocity and hence low value of inertia of motion. Due to it, they are able to go around and bend easily.

**Q. 14. Are Kirchhoff’s laws applicable to both a.c. and d.c.?**

**Ans.** Yes, Kirchhoff’s laws are equally applicable to a.c. as well as d.c. circuits.

**Q. 15. State the basic concept on which two Kirchhoff’s laws are based.**

**Ans.** Kirchhoff’s first law is based on the fact that the charges are not accumulated at a junction. Kirchhoff’s second law supports the law of conversation of energy.

*Q. 16. Kirchhoff’s first law obeys law of conversation of charge. Explain.*

**Ans.** According to Kirchhoff’s first law, the current (I_{1}) entering a given junction of the circuit in a certain time (t) = current (I_{2}) leaving the junction during the same time (t). So; I_{1 }t = I_{2} t or q_{1} = q_{2}, i.e., charge entering the junction is equal to the charge leaving that junction.

**Q. 17. What are the difference between Kirchhoff’s 1 ^{st} and 2^{nd} laws?**

**Ans.**

S.N. | First Law | S.N. | Second Law |

1. | This law supports the law of conversation of charge. | 1. | This law supports the law of conversation of energy. |

2. | According to this law | 2. | According to this law |

3. | This law can be used in open and closed circuits. | 3. | This law can be used in a closed circuit. |

## Summery | Highlight of DC Network Analysis

- An electric circuit (or network) is an interconnection of physical electrical devices such as an energy source (or sources), an energy convertor or convertors (load or loads), and conductors that connect them.
- A junction (or node) is a point in a network where two or more branches meet.
- A loop is a closed path in a network formed by a number of connected branches. Mesh is a loop that contains no other loop within it.
- A voltage source of voltage V
_{s}and internal resistance R_{in}can be converted into an equivalent current source of current I_{s}= V_{s}/R_{in}and a resistance R_{in}across it. Similarly, a current source of output current I_{s}in parallel with resistance R_{in}can be converted into an equivalent voltage source of voltage V_{s}= l_{s}R_{in}and a resistance R_{in}in Series with it.

A voltage source-series resistance combination is equivalent to a current source-parallel resistance combination if, and only if their respective open-circuit voltages are equal, and their respective short-circuit currents are equal.

- According to Kirchhoff’s first law (or current law), the algebraic sum of currents in two or more conductors at a point (junction) is always zero

i.e.

While applying above law, incoming currents are taken as positive and outgoing currents as negative.

According to Kirchhoff’s second law (or voltage law), the algebraic sum of emfs acting in any closed circuit or mesh is equal to the algebraic sum of the products of currents and resistances of each part of that closed circuit or mesh i.e.,

- According to Superposition theorem if there are a number of Voltage and current sources acting simultaneously in any linear bilateral network, then each source can be considered acting independently of the others.
- In loop method of analysis, independent mesh currents are taken and the network is solved by framing equations according to Kirchhoff’s second or voltage law (KVL).
- In nodal analysis, independent nodes are considered and Voltages are assumed at these nodes w.r.t. one reference node, called the datum node. The equations are framed according to Kirchhoff’s current law (KCL) which reveal the desired results after their Solution.
- Thevenin’s theorem may be stated as follows:

The current in any passive circuit element (which may be called R_{L}) in a network is the same as would be obtained if R_{L} were supplied with a source voltage V_{oc} or V_{T} in series with an equivalent resistance R_{in} or R_{T}, V_{oc} being the open-circuit voltage at the terminals from which R_{L} has been removed and R_{T} being the resistance that would be measured at these terminals after all sources have been removed and each source has been replaced by its internal resistance.

- Norton’s theorem is an alternative to Thevenin’s theorem. According to this theorem, any two-terminal active network, when viewed from output terminals is equivalent to a constant current source in parallel with a resistance.
- According to Reciprocity Theorem, if the source voltage and zero-resistance ammeter are interchanged, the magnitude of the current through the ammeter will be the same, no matter how complicated the network.
- Maximum power transfer theorem states that a resistive load, served through a resistive network, will abstract maximum power When the load resistance value is the same as the resistance “viewed by the load as it looks back into the network”.
- Millman’s theorem is a combination of Thevenin’s and Norton’s theorem and enables a number of voltage (or current) sources to be combined in a single voltage (or current) source.

- According to Tellegen’s theorem the summation of instantaneous powers for the n branches in an electric network is always zero.

i.e.

- In delta-star transformation, the equivalent Star resistance connected to a given terminal is equal to the product of the two delta resistances connected to the same terminal divided by the sun of the delta connected resistances.
- In star-delta transformation, the equivalent delta resistance between two terminals is the sum of the two star resistances by the third star resistance.