 Hello everyone, myself Sanjay Udge, Assistant Professor, Department of Electronics Engineering, Valchand Institute of Technology, Solapur. Today, we are going to discuss Numerical on DC Circuit Part 1. Learning outcome. At the end of this session, students will be able to analyze and simplify series and parallel DC circuits. Guidelines. Introduction. Numericals on DC circuits. Assignment. References. Introduction. Series circuits. All the resistances are connected back to back such that same current flows through all the resistances. Let us take example number 1. In the following circuit, calculate the total current I t taken from the 12 volt supply. So, the circuit consists of this 12 ohm resistance at the last branch on the right hand side, then this 8 ohm, then a 4 ohm, then 6 ohm. So, what you will find over here? These two resistances are in series. So, these two resistances are series. We can add these two resistances. So, it will be 8 plus 4 12. This 12 ohm resistance is coming parallel with the another 12 ohm resistance. So, how to solve this circuit? So, where to find out the total current? So, the supply or voltage source is always shown on the left hand side. These are the resistances to find out the total current. Remember, we are finding out the total current. To find out the total current, we must find out the equivalent resistance of the given network, which consists of a 12 ohm parallel to these two series resistances and then they are coming in series with this 6 ohm resistances. We can see that the two resistors R 2 and R 3 are actually both connected together in a series combination. So, we can add them together to produce an equivalent resistance in that branch. The resultant resistance for this combination would therefore, be R 2 plus R 3 is equals to 8 ohm plus 4 ohm is equals to 12 ohm. So, we can replace both resistor R 2 and R 3 above with a single resistor of resistance value 12 ohm. So, the circuit will look like this. In this branch, there were earlier two resistances 8 and 4 in series. So, adding these two, we get the 8 plus 4 12 ohm resistance. Now, the picture is this 12 ohm and 12 ohm R A and R 4, they are coming in parallel, which carries the currents I 1 and I 2. So, now let us find out the equivalent resistance of these two branches. So, our circuit now has a single resistance R A in parallel with the resistance R 4. Using our resistors in parallel equation, we can reduce this parallel combination to a single equivalent resistor value of R combination using the formula for two parallel connected resistors as follows. R combination is equal to 12 ohm parallel 12 ohm. So, the formula for this is R 1 into R 2 upon R 1 plus R 2. So, R combination will be equals to 12 into 12 upon 12 plus 12 is equals to 6 ohm. That means, if the two resistance are having same value in parallel, the net resistance will be R by 2. So, 12 parallel 12 will become 6 ohm. R 1 and R combinations are connected together in a series combination and again they can be added together resistors in series. So, that the total circuit resistance between points A and B is therefore, given as R A B is equals to R combination plus R 1 is equals to 6 ohm plus 6 ohm is equals to 12 ohm. Using Ohm's law, the value of the total current flowing around the circuit is calculated as I total is equal to total supply voltage 12 volts divided by 12 ohm that is I is equal to V upon total voltage upon total resistance or equivalent resistance. So, total current comes out to be 1 ampere. Example number 2, we are having R 1, R 2, R 3, R 4, R 5, R 6, R 7, R 8, R 9 and R 10. So, this is the combination of again series and parallel networks. This resistor ladder network may seem a complicated task, but as before it is just a combination of series and parallel resistor connected together. Starting from the right hand side and using the simplified equation for two parallel resistors, we can find out equivalent resistance of the R 8 and R 10 combination and call it as R A. So, to find out the equivalent resistance between points A and B, let us start solving this ladder network from the right mode side. So, this shaded portion is the R A resistances in which 10 and 2 they are in series because same current close through this. So, it will be 12 ohm 10 plus 2 12, 12 will be now in series with this 6 ohm. Solving this 12 and 6 parallel network, it will come in series with this 8 ohm. So, in this way we are going to solve this resistive network which is a combination of parallel and series. We will come at this resistance 6 ohm with the equivalent plus the in series with the remaining network. R A is equals to R 9 into R 8 plus R 10 divided by R 9 plus R 8 plus R 10 is equal to 6 into 12 upon 6 plus 12 4 ohm. So, the shaded portion will have the value equals to 4 ohm because 6 ohm now in it is in parallel with the 10 plus 12 ohm, 6 parallel 12 ohm. So, R A comes out to be 4 ohm. Now, redraw the circuit let us denote this shaded portion as R B. This 4 ohm now will come in series with the 8 ohm resistance. So, 4 plus 8 it will be 12. So, R B will now it will become 12. This 12 ohm now will come in series with the 6 ohm resistance. So, R B will be equals to 12 parallel 6 that is R B equal to 12 into 6 divided by 12 plus 6. So, R B comes out to be 4 ohm R B in series with the R 5 therefore, total resistance will be R B plus R 5 4 plus 4 8 ohm. This resistive value of 8 ohm is known in is now in parallel with R 4 and can be calculated as R C as shown R C is equals to 4 ohm R C is in series with R 3 therefore, the total resistance is R C plus R 3 8 ohm. This resistive value of 8 ohm is now in parallel with the R 2 from which we can calculate R D is equals to 4 ohm. R D is in series with R 1 therefore, the total resistance R D plus R 1 is equal to 4 plus 6 10 ohm. Thus the complex combinational resistive network above comprising of 10 individual resistors connected together in series and parallel combinations can be replaced with just one single equivalent resistance R equivalent that is R A B of value 10 ohm. Question, what is the difference between series and parallel circuit? Series circuit voltage get divided across the all resistances depending on the value of the resistance. In parallel circuits current get divided across all the resistances again this current across all the parallel resistances depends on the value of the resistance.