*Target Audience: High School Students, College Freshmen and Sophomores, Class 11/12 Students in India preparing for ISC/CBSE and Entrance Examinations like the IIT-JEE Main or Advanced/AIEEE, and anyone else who needs this Tutorial as a reference!*

*Here's a quick outline of what we'll introduce in this tutorial. The omplete tutorial document (PDF) is provided at the end.*

**Circuit theory**

This tutorial is the first in the series for the course circuit theory. This tutorial has the following contents. :Introduction to Electrical Engineering, DC systems, Kirchhoff’s laws, Capacitance.

**Electric charge**

In all atoms there exists number of electrons which are very loosely bounded to its nucleus. Such electrons are free to wander when specific forces are applied. If any of these electrons is removed, the atom becomes positively charged. And if excess electrons

are added to the atom it becomes positively charged. The total deficiency or addition of electrons in an atom is called its charge. A charged atom is called Ion. An element containing a number of ionized atoms is said to be charged. And accordingly the element consisting of that atom is said to be positively or negatively charged.

**Electric Current (I)**

All electrons in an atom have certain potential energy. Given a suitable medium in which to exist, they move freely from one energy level to another when small external effort is applied. And this flow takes place from higher energy level to lower energy level. A negative terminal is higher energy level for electron and lower energy level for proton. Similarly a positive terminal is higher energy level for proton and lower energy for neutron. Electricity is the flow of charge. Conventionally the flow of protons from positive terminal to negative terminal is considered as Electric current.

**Resistance (R)**

It is the property of electric circuit resisting or preventing the flow of electrons (current). Due to resistance some electrical energy is lost as heat. It depends on various factors. Unit of resistance is Ohm (Ω)

**Electromotive force (EMF)**

It is the voltage generated by a battery and is measured in volts. EMF is not a force but the work done in moving +1 C charge around a circuit. The EMF pushes the electrons through the wires of the circuit. It is denoted by E.

**Potential difference (V)**

Potential of a particle at a point is the amount of work done in bringing that particle from infinity position to that point. Hence potential difference between two points is defined as the difference in their potential. And accordingly, there exists either repulsive or attractive force between them which is caused by potential difference. Two like charged particles attract each other and unlike charges repel each other. It is also mmeasured in volts and is denoted by V.

**Ohm’s law**

V= I R where R is the constant and is equal to resistance of the conductor. Ohms law is not applicable for non metallic conductors and for non linear devices.

Circuits consisting of two or more resistance connected in series to a source are called series circuits. Two resistances in series carry same amount of current. And the voltage supplied is equal to the sum of the voltage drop across each resistance.

**Parallel Circuits**

Circuits consisting of two or more resistance connected in parallel to a source are called parallel circuits. Two resistances in parallel dissipate same amount of voltage. And the total current given out from the source is equal to the sum of the voltage drop across each resistance.

**Kirchhoff’s Laws:**

**Kirchhoff’s current law:** The total current entering into any node (junction) has to be equal to the total current leaving out that node (junction). This is true for any node in a circuit, no matter how many branches lead into or out of the node. It can also be stated as the algebraic sum of currents entering into a node is zero. Different signs are given to currents going into the junction and out of the junction.

**Kirchhoff’s voltage law: **In a closed loop, the algebraic sum of the voltages drops is equal to the Voltage sources acting round the loop.

**Capacitance**

A capacitor stores the energy in form of electrostatic field. It is denoted by C and it is measured in Farads (F). The common form energy storage is parallel plate capacitor. If the charges on the plates are +Q and –Q, V is the voltage between two plates then, C = Q/V.

For two capacitors connected in series: The current passing through the circuit is denoted by i. In series connection, voltage changes but current remains the same.

For two capacitors connected in parallel: The current passing through C1 is i1 and the current passing through C2 is i2. In a parallel connection, the voltage remains the same, but the current varies.

*Here are some of the questions solved in this tutorial :*

**Q: **A resistor dissipates energy at the rate of 40 W and the current in it is 20 A. Determine the energy of each coulomb of charge in the circuit.

**Q: **A 200 ton locomotive experiences wind resistance equivalent to 62.5 N/ton. The efficiency of driving motors is 87% and the cost of electrical energy is 8p/kWh. What is the cost of the energy required to make the train travel 1km? If the train velocity is 80km/h and the supplied a constant voltage of 1.5 kV, determine the supply current.

**Q: **In general DC systems consist of only resistor elements. Capacitors acts as open circuit to DC supply and Inductor elements act as short circuit for DC voltage supply. Hence in this unit we only see circuits consisting of resistor elements.

**Q: **A 220v supply is applied across two resistances 10kΩ and 20kΩ each in series. Find the current in the resistances.

**Q: **Find the total current when two resistances 10 Ω and 20 Ω are connected in series and parallel across a supply of 100 V.

**Q:** A 200 ton locomotive experiences wind resistance equivalent to 62.5 N/ton. The

efficiency of driving motors is 87% and the cost of electrical energy is 8p/kWh. What is the

cost of the energy required to make the train travel 1km? If the train velocity is 80km/h and

the supplied a constant voltage of 1.5 kV, determine the supply current.

**Q:** A 220v supply is applied across two resistances 10kΩ and 20kΩ each in series. *Find the current in the resistances.*

**Q: **Three resistances 8Ω, 4Ω, 2Ω are in series. A current of 1A is flowing through *them. Find the voltage across each resistor and also total supply.*

**Q: **A 100v supply is applied across two resistances 10 and 20 in parallel. Find the *currents through each resistance. And find the effective resistance.*

**Q:** Find the total current when two resistances 10 Ω and 20 Ω are connected in series *and parallel across a supply of 100 V.*

*Q: *Calculate the amount of voltage between points A and B in this circuit. And *identify polarities and voltage magnitude at those points.*

**Q: **Find the total capacitance when three capacitors of 2, 4 and 8μF are connected in *i) series ii) parallel*

*... and many other interesting questions. *

**Complete Tutorial With Solved Problems :**

**Related Tutorials ( Introduction to Electrical Circuits - DC ) :****Circuit Theory 1a - Introduction to Electrical Engineering, DC Circuits, ****Resistance and Capacitance, Kirchoff Law**
| Resistors, Capacitors, problems related to these. | **Circuit Theory 1b - More solved problems related to DC Circuits with Resistance and Capacitance**
| Capacitors,
computing capacitance, RC Circuits, time constant of decay, computing
voltage and electrostatic energy across a capacitance | **Circuit Theory 2a - Introducing Inductors**
| Inductors,
inductance, computing self-inductance, flux-linkages, computing energy
stored as a magnetic field in a coil, mutual inductance, dot
convention,
introduction to RL Circuits and decay of an inductor. | **Circuit Theory 2b - Problems related to RL, LC, RLC circuits**
| Introducing the concept of oscillations. Solving problems related to RL, LC and RLC circuits using calculus based techniques. | **Circuit Theory 3a - Electrical Networks and Network Theorems**
| Different
kind of network elements: Active and passive, linear and non-linear,
lumped and distributed. Voltage and current sources. Superposition
theorem, Thevenin (or Helmholtz) theorem and problems based on these. | **Circuit Theory 3b - More network theorems, solved problems**
| More
solved problems and examples related to electrical networks. Star and
Delta network transformations, maximum power transfer theorem,
Compensation theorem and Tellegen's Theorem and examples related to
these. |