In the last lesson, we had a discussion on KCL and now we are going to understand what is KVL (Kirchhoff’s voltage law) and how to apply KVL.

So let’s move on to the statement of KVL, “The algebraic sum of all the voltages in any closed loop is zero”. So when you calculate the algebraic sum of all the voltages. This means you calculate the sum of all the voltages considering their signs then you will find it is equal to zero in a closed loop. For example, here we have a closed-loop having three elements,

How to apply KVL

Now we know the fact that when current I pass through a resistance R1 there will be a voltage drop and the voltage drop will be equal, to I x R1 (following the ohm’s law) R1 and R2 are connected in series, therefore the same current I will flow through R2 as well and therefore the voltage drop across R2 to will be equal to I x R2.

So, V – IR1 – IR2 = 0

This is our KVL equation.

Here we have followed the convention in which we are considering the rise in potential as positive (+) and the drop in potential as negative (-).

So the convention is the rise in potential will give you the positive sign and a drop in potential will give you the negative sign.

Now we will move on to the last point and according to this point the KVL is based on the law of conservation of energy KCL was based on the law of conservation of charge but KVL is based on the law of conservation of energy. The voltage is the measure of potential energy difference across the element we know this point and we also know that there is a single unique value of a voltage therefore the energy required to move a unit charge from one point to other is independent of the path chosen you will get the same voltage potential difference between the two points irrespective of the path you have chosen.

The first kirchhoff’s law is Kirchhoff’s current law in short known as KCL and the second Kirchhoff’s law is Kirchhoff’s voltage law in short known as KVL and these two laws were given by Gustav Kirchhoff a German physicist and in this lesson will discuss KCL and in the next lesson will talk about KVL.

Now according to KCL, “the algebraic sum of the currents entering any node is zero”. Let’s try to understand the meaning of this statement. whenever you calculate the algebraic sum of the currents which are entering a node then you will find the algebraic sum is equal to zero. So what do we mean by algebraic sum is the aggregation of two or more quantities taken with regard to their sign. So here we are calculating the algebraic sum of the currents. This means we will calculate the sum of currents with their signs and when you calculate the sum of currents with signs you will find it is equal to zero at any node. Now you have to follow one convention according to the convention: the current which is entering or we can say the entering current will have the positive sign (+) and the leaving current will have the negative sign (-). So this is the convention that will follow in case here and this convention is opposite in nodal analysis but for now, just remember this convention that the entering current will have the positive sign and the leaving current will have the negative sign and I will take one example.

How to apply KCL

In this example, we are having this node and you can see that five currents are meeting at the node.

Current I1 is the entering current. Current I2 is the leaving current. Current I3 is the entering current I4 is also the entering current and I5 is the leaving current. So two currents I2 and I5 are the leaving currents and the remaining three currents I1, I3 and I5 are the entering currents. Now we will calculate the algebraic sum of the currents this means we will add all the currents

Entering Current = +

Leaving Current = –

We can see that,

sum of entering currents = sum of leaving currents So remember this point that the sum of entering currents will be equal to the sum of leaving currents. This is one important point. Now let’s understand why we are getting the algebraic sum is equal to zero at node. We know node is not a circuit element and therefore it cannot store the charge and also destruction and generation of charge is not possible according to the law of conservation of charge. So this particular statement is based on the law of conservation of charge + the fact that node is not a circuit element. Because of these two points node will not be able to store the charge. It will not be able to generate the charge and also it will not be able to destroy. Now the current entering means the charges are entering and the number of charges entering to this node must be equal to the number of charges leaving the node.

Economics is the study of how humans make choices and limited resources and conditions of scarcity. These decisions can be made by individuals’ families and businesses of societies. It is a social science related to the production, distribution and consumption of goods and services. It helps study how individuals, businesses, governments and nations make choices on allocating resources to satisfy their wants and needs, trying to determine how these groups should organise and coordinate efforts to achieve maximum output. As an example, when we are evaluating the interest rate on our credit cards or trying to decide whether to buy or lease a house or purchase something, these are all decisions we make using economic thinking. We live in a world of limited resources and economics helps us decide how to use these limited inputs to satisfy our wants and needs.

2. Economics is considered Social science? Do you agree? Explain?

Mainly the science we can group into two broad categories that especially difference each other

· Pure Science

· Social Science

Pure science is a science that derives theories and assumptions. Pure science can also be known as Natural science or fundamental science. It deals with the study of natural phenomena through observation, experimentation, and the use of the scientific method.

Social science is a branch of science devoted to the study of societies and the relationship among individuals within those societies. Study of the behaviour of people such as individuals, groups of peoples, firms, societies, or economics, and there are individuals or collective behaviour.

Economics studies human behaviour, collecting facts, scientifically analysing them and formulating a theoretical base to explain human behaviour. Therefore, it is a social science. So, yes. I agree with “economics is considered as a Social science”

3. Briefly discuss why do you study Economics

Economics helps to make decisions to satisfy limited resources and conditions for scarcity. We can explain the importance of studying Economics in two different paths.

1. individual point of view

In day to day life, we face numerous problems to be solved individually. As an example, how can we spend money, how can a business firm decide maximum output, how can we get maximum profit, and how can we minimise business uncertainty. So if you know Economics, it may help to make good decisions for the greatest satisfaction.

2. The social point of view

The more policymakers know about economics, the better they can decide solutions to minimise the economic problems and maximise the living conditions of the nation.

4. Distinguish between micro and macroeconomics

Microeconomics relates to the study of the behaviour of individual economic units such as individual consumers, business firms, commodities, etc. Microeconomics gives us a microscope view of the economy.

Macroeconomics studies the behaviour of not a particular company, or Industries but the whole economy. It includes understanding how unemployment, price levels, and growth rates affect the economic aspect such as the gross national product (GNP). Macroeconomics gives us a bird’s-eye view of the economy.

5. What do you mean by opportunity cost? Explain this using examples.

Opportunity cost is the value of the next best alternative which is a foregone Choice that leads to the sacrifice of one need for another need. This arises due to scarcity of resources.

In the case of a consumer, she/he has to scarify the consumption of another commodity, in order to increase the consumption of the one commodity.

Example: – A passenger takes public transport to work instead of driving. It takes 2 hours on public transport, while driving takes 1 hour and 40 minutes. The opportunity cost is 40 minutes spent elsewhere each day.

6. Explain the following as factors of production.

· Labour

· Capital

Labour means any type of physical or mental effort. In Economics terms, labour is the effect exerted to produce any goods or services. It includes all types of human efforts-physical exertion and mental exercise, use of intellect, etc. done in exchange for an economic reward.

Capital is an important factor in production. It consists of those goods which are produced by the economic system and are used as input in the production of further goods and services. Capital comprises one of the four major factors of production.

7. What is the production possibility curve?

The production possibility curve is a curve that illustrates the variation in the amounts that can be produced for two products if both depend upon the same finite resource for their manufacturer. It measures the maximum output of two goods using a fixed amount of input.

Fluid Mechanics is that discipline in the broad field of applied mechanics that is concerned with the behavior of liquids and gasses at rest or in motion.

It covers a vast array of phenomena that occur in nature (with or without human intervention.)

* Fluid cannot offer permanent resistance to a deforming (shearing force)

Fluids flow How when acted upon by a shearing (deforming) force, deforming continuously for as long as the force is applied.

* A Fluid is a substance that deforms continuously under the action of shearing forces, however small they may be.

Conversely, it follows that ;

If a fluid is at rest, there can be no shearing force acting and therefore, all forces in the fluid must be perpendicular to the planes upon which they act.

Properties of Fluid

Density or Mass Density

The density or mass density of a fluid is defined as the ratio of the mass of a fluid to its volume. Thus mass per unit volume of a fluid is called density. The density of a liquid may be considered constant while that of gasses changes with the variation of pressure and temperature.

Specific Weight or Weight Density

Specific weight or weight density of a fluid is the ratio between the weight of a fluid to its Volume. Thus weight per unit volume of a fluid is called weight density.

Specific Volume

The specific weight of a fluid is defined as the volume of a fluid occupied by a unit mass or the volume per unit mass of a fluid is called specific volume.

Viscosity

Viscosity is defined as the property of a fluid that offers resistance to the movement of one layer of fluid over another adjacent layer of the fluid. When two layers of a fluid, a distance apart, move one over the other at different velocities see u and du as shown in the figure, the viscosity together with relative viscosity cause stress acting between the fluid layers. The top layer causes shear stress on the lower layer while the lower layer causes the shear stress on the adjacent top layer. This shear stress is proportional to the rate of change of velocity with respect to Y.

Kinematic Viscosity

It is defined as the ratio between the dynamic viscosity and the density of the fluid.

Newtonian and Non-Newtonian Fluids

The shear stress (𝜏) on a fluid element layer is directly proportional to the rate of shear strain. The constant of proportionality is called the coefficient of viscosity.

Fluids that obey the above relation are known as Newtonian fluids and the fluids which do not obey the above relation are called Non-newtonian fluids.

A system of conductors and components forms a complete path current for flow.

Properties of an electrical circuit including

Voltage (Volts/V)

Current (Amps/A)

Resistance (Ohms/Ω)

Current Flow

The conventional current that assumes current flows out of the positive side of the battery, through the circuit & back to the negative side of the battery. This was the convention established when electricity was first discovered, but it is incorrect.

Voltage (V) – the force (pressure) that causes current flow.

Resistance (Ω ) – material’s tendency to resist the current.

Ohm’s Law

Current in a resistor varies directly proportional to the voltage applied to it and inversely proportional to the resistor’s value.

Current

Current is a rate of flow of charges.

Why does the current flow?

A voltage source provides the energy (or work) required to produce a current.

A source takes charge particles (usually electrons) and raises their potential. So they flow out in one terminal into and through a transducer (light bulb or motor) on their way back to the source of the other terminal.