 Hello, everyone. Welcome to our video lecture on registers in parallel. Myself, K. R. Biradar, assistant professor, department of electronics and telecommunication engineering, Walsh and Newstab technology, Swalapur. Let us start with the learning outcomes first. At the end of this session, we will be able to justify the circuit behavior when registers are connected in parallel. Introduction registers when connected in a circuit that connection may be either series or parallel. What happens with the voltage and current when resistances are connected in parallel? We shall see those things in this video. Resistances in parallel. Resistance are said to be connected in parallel when both of their terminals are respectively connected to each terminal of the other register or registers. See this diagram. There is a voltage source is connected. There are 3 resistances R1, R2 and R3 which are connected in parallel. The current flowing across this circuit here it is I and it divides as I1, I2 and I3. I1 is across the R1, I2 is across the resistance R2 and I3 is across the resistance R3. In this case, the total current I that leaves the battery is split into 3 separate paths. Therefore, I equal to I1 plus I2 plus I3. Therefore, the equivalent resistance when connected in parallel. In this diagram, resistance are the equivalent resistance when 3 resistances are connected in parallel. Therefore, it is Rp. Rp is the total or effective resistance when connected in parallel. Again, there is a battery or voltage source and current flowing across this is I and Rp is the total or effective resistance. Expression for registers in parallel. Total current I in the circuit is equal to the sum of currents through each of 3 resistances. Therefore, I equal to I1 plus I2 plus I3 in the circuit diagram. Since the voltage across each register is the same, applying Ohm's law to each register we have I1 equal to V divided by R1. So, voltage will be same that is resistance R1. Similarly, I2 which is flowing across R2, I2 equal to V divided by R2. Similarly, I3 equal to V divided by R3. If I substitute I1, I2 and I3 in main current I, therefore, I now becomes equal to V divided by R1 plus V divided by R2 plus V divided by R3. Again, this is equal to if I take V common V into 1 divided by R1 plus 1 divided by R2 plus 1 divided by R3. This is also equal to V divided by Rp. Therefore, 1 by Rp equal to 1 divided by R1 plus 1 divided by R2 plus 1 divided by R3. That means, 1 by R1 plus 1 by R2 plus 1 by R3 will be replaced by 1 by Rp. Here, Rp refers to equivalent resistance when connected in parallel. The value of equivalent resistance in parallel connection will be lesser than each individual resistance. That means, equivalent resistance when connected in parallel their value will be reduced. Take one problem. Calculate the equivalent resistance in the following circuit and also find the current I1, I2 and I3 in the given circuit. This is a circuit diagram having battery or voltage source equal to 24 volt and there are two resistance are connected R1 and R2 which are in parallel having values R1 equal to 4 ohm and R2 equal to 6 ohm. The current flowing from this battery is I. I will be split at this position as I1 and I2. Since the resistors are connected in parallel, the equivalent resistance in the circuit is 1 divided by Rp which is equal to 1 divided by R1 plus 1 divided by R2. So, R1 he has given equal to 4 and ohm and R2 equal to 6 ohm. 1 by R1 by 1 by 4 plus 1 by R2 by 1 by 6 you take the LCM and this comes out to be 5 divided by 12 ohm. This 5 divided by 12 ohm is equal to 1 by Rp. Therefore, Rp equal to take the reciprocal of it becomes 12 divided by 5 ohm. The resistors are connected in parallel the voltage across each resistor is same. Therefore, I1 equal to V divided by R1. V is same in both the resistors, but substitutes its value equal to 24 volt divided by R1 equal to 4 ohm. So, this is equal to 6 ampere. Similarly, I2 equal to V divided by R2. Substitute V equal to 24 R2 equal to 6 ohm which comes out to be 4 ampere. The total current in two branches I equal to I1 plus I2. I1 equal to 6 ampere and I2 equal to 4 ampere, 6 plus 4 which is equal to 10 ampere. Similarly, we shall see one more example here. Calculate the equivalent resistance between A and B in the given circuit. From the point A and B, there are 6 resistors are connected. So, 2 ohm and 2 ohm are in parallel. So, 4 ohm and 4 ohm are in parallel and 6 ohm and 6 ohm are in parallel. Once if you know simplify this parallel resistance, then all three comes in series. Let us consider the first parallel combination. We can say it is a part 1. In part 1, this 2 ohm and 2 ohm are in parallel. Therefore, their equivalent resistance is I consider 1 divided by RP1 which is equal to 1 divided by R1 plus 1 divided by R2. R1 here is 2 ohm and R2 is also 2 ohm. It is 1 by 2 plus 1 by 2. This comes out to be 1 ohm. That means, RP is the combination of these two parallel resistance, their equivalent resistance equal to 1 ohm. Similarly, second parallel connection that 4 ohm and 4 ohm are in parallel. Therefore, their 1 divided by RP2 is the equivalent resistance for these two 4 ohm resistors which are connected in parallel is equal to 1 divided by R1 plus 1 divided by R2. R1 is 4 and R2 is also 4, 1 divided by 4 plus 1 divided by 4. So, if I simplify this RP comes out to equal to 2 ohm. So, the third part it is 6 ohm and 6 ohm resistance are in parallel these two resistances. Their equivalent resistance I will consider RP3 1 divided by RP3 equal to 1 divided by R1 plus 1 by R2, 1 by 6 plus 1 by 6. So, therefore, RP becomes equal to 3 ohm. Between the terminals A and B, we have found out RP1 is a combination of 2 ohm and 2 ohm that is first part and RP2 also you have calculated, RP3 also calculated. RP1, RP2 and RP3 comes in series now. Therefore, series connections now RP1 and RP2, RP3 are connected in series. Therefore, RP total or effective resistance RP equal to RP1 plus RP2 plus RP3. If I sum it up it comes out to be 6 ohm because RP1 equal to 1 ohm, RP2 equal to 2 ohm, RP3 equal to 3 ohm. So, 1 plus 2 plus 3 equal to 6 ohm. The equivalent resistance between points A and B is 6 ohm. These are the references used to prepare above PPT. Thank you.