Resistances in series and parallel | NEET JEE MAINS |

Ajouté : 2026-05-20

[00:00:01]Okay.

[00:00:04]Now just see here. So what is the basics of this current?

[00:00:10]The basics of this current electricity is first of all what is the meaning of resistance.

[00:00:24]Let us discuss what is the basic of this. Okay. So you all know that resistance is directly proportional to length. Resistance is inversely proportional to cross-sectional area and resistance is directly proportional to L by A. Resistance is equal to row L by A.

[00:00:41]This is the basic concept of resistance.

[00:00:43]You all know about that, isn't it? H.

[00:00:46]Okay. So from this what do you understand? If the wire is having length L1, if the length of the wire has been doubled, if L1 is L, L2 is 2 L. Okay?

[00:01:00]And area of cross-section is same, then what happens to the resistance?

[00:01:06]When length is doubled, what happens to the resistance?

[00:01:10]H >> double doubled. Length is also doubled means what happens to the resistance? It is also double because it's a direct relation.

[00:01:19]For example, if length is same, if length is same, area of the area of cross-section of the wire is a first, then area has become 2, doubled, area has been doubled. What happens to the rest then?

[00:01:35]>> Huh? Length is same, material is same, material is same row is same here. Okay, row means specific resistance. Specific resistance is constant for a particular material, isn't it? So this is a basic concept that resistance is inversely proportional to cross-sectional area. If area is doubled the resistance becomes half. You know about this isn't it up to here it's okay. Then the next thing is cross-sectional area can be considered as p<unk> r². Am I right or not? You can take it as p<unk> r². Okay. So then what else you'll be getting now? Resistance is equal to row l by pi r². So what do you understand from this? Resistance is inversely proportional to r².

[00:02:16]Okay. Then resistance is inversely proportional to radius of the wire. So if radius is doubled, what happens to resistance?

[00:02:24]>> Four times 1 by 4 * inverse relation.

[00:02:30]See here if r1= r2 = 2 r that means r2 by r1 = r1 by r2² right or it's a inverse relation.

[00:02:44]Is it not an inverse relation here? Do you understand what I'm saying? Now it's inverse relation. So if the resistance of the wire is R, if has been doubled, it has become 2 R. Then what happens to the resistance? R2 by R1 is equal to R1 by R2. R1 is R. R2 is 2 R is going to be square. So therefore R2 by R1 is going to be 1x4. That means R2 is equal to R1 by 4. This is a simple concept, isn't it? Simple concept.

[00:03:16]Everyone knows about this, isn't it?

[00:03:18]Everyone knows about this. But what happens? See, this is applicable when extra length is added.

[00:03:26]This concept is applicable.

[00:03:29]Already there is a wire. Extra length is added here.

[00:03:33]Already is there. Extra area is added to that.

[00:03:37]Extra extra extra. Then these formulas are applicable. What are the formulas applicable for extras?

[00:03:44]Okay, the for extras the first relation is R is directly proportional to length.

[00:03:51]The second relation is R is inversely proportional to area. The third relation is R is inversely proportional R². This is applicable only when present length extra length is added present area extra area is add extra.

[00:04:07]If it is not extra, if it is not extra, already there is a wire here. Okay, already there is a wire.

[00:04:16]Okay, this much wire is there. I'm not adding any extra length to that. The same wire I am melting and stretching.

[00:04:27]Same wire I'm melting and stretching.

[00:04:31]Previously area was A1. Now area has become A2. Previously length is L1 length increases, area of cross-section decreases.

[00:04:42]But what is going to be same here?

[00:04:45]What is same here?

[00:04:48]Volume is same. This is a cylinder. No, how much material you are using here?

[00:04:56]The same material is present here also.

[00:04:58]So volume is same. So volume is remaining constant in both the cases.

[00:05:02]Volume is same. So what I'm saying is okay so in stretching cases these are all you just remember it is uh these are all stretching cases not extra length is added whatever the left is present that has been pulled that's it no nothing from outside the same length has been the same wire is changing to different dimensions then what happens what happens to the length First of all, so for that you just remember R= L by A and you all know volume is equal to area and length.

[00:05:45]I want what is the relation between resistance and length? I don't want area.

[00:05:50]Then should I not replace this area? Now area should be removed. I don't want the relation between area. I want the relation between length and resistance in the stretching cases. For that what I'll do? Instead of area I will take volume by length. So I'll substitute here. Now then what I'm going to get?

[00:06:08]Resistance is equal to row L by A. A means V by L. So R is equal to row L² by V. So in this case in this case what is going to be constant?

[00:06:22]Volume is going to be constant. Isn't it? Volume is going to be constant. So create a formula in which length is present which is a variable and add one extra physical quantities which is a constant and row is already constant because it is a we are not changing any material right or not you are not changing any material. So from this what do you understand resistance is directly proportional to L² new relation. So this is where childrens are going to get confused.

[00:06:52]What happens when resistance is doubled?

[00:06:55]What happens when length is doubled means you write is doubled but you won't read in the question that the wire has been melted and doubled its length by stretching then you can't use the same relation R is directly proportional to L you should use the relation R is directly proportional to L square that you should remember volume is constant row is constant that's the case here there are many previous questions related to that the next thing is here.

[00:07:28]This is a Y. This is a Y. Okay. Now we are considering that you are your melting and your stretching. Then previously length was L1 length was L2 volume was same area was A1 here it is A2. So now the same formula I'm using ro by A. Now I don't want the relation between resistance and length. I want the relation between resistance and area now. Okay. And volume is constant here.

[00:08:01]So what I'm going to do volume is equal to area into length. Okay. And I don't want length. I should replace length. No length can be taken as volume area.

[00:08:13]Length can be taken as volume.

[00:08:16]>> So therefore resistance is equal to row here means what will you write? V by A / A. So resistance is going to become row V by A². So in this I have created one variable two constants. I told you that when you stretch something volume going to be constant specific resistance is any constant because I'm not adding any extra all same material only stretching is there. So here there are two constants. There are two constants. Row is constant. V is constant. Now I got a new relation. Resistance is inversely proportional to A². Not like extra length added or extra area added. In extra area added, R is inversely proportional to area. But while stretching cases, R is directly proportional to L². R is inversely proportional to A². And one more thing is you all know area is nothing but R².

[00:09:12]So resistance is inversely proportional to<unk> R².

[00:09:17]So resistance is inversely proportional to R power 4. In specially stretching cases the relation between resistance and radius is nothing but hu it is inversely proportional to R power 4. In the previous case, in the previous case, what is going to happen?

[00:09:35]In stretching cases, in without stretching cases, R is inversely proportional to R² just extra length added, extra area added inversely proportional to R². But this is a special case. Stretching cases then R is inversely. So what are the new relations we got?

[00:09:56]The first thing is I got a relation R is directly proportional to L². If length is doubled, resistance become four times.

[00:10:03]Okay. Now this is the next relation is R is inversely proportional to A².

[00:10:10]When area is made to half when area becomes half then what happens to resistance? It becomes four times inverse relation. You know it becomes what?

[00:10:25]Previously if it becomes half radius become resistance becomes double without stretching only extra length added. But here what happens?

[00:10:35]Area becomes half resistance become four times stretching cases. Then what about radius?

[00:10:43]If radius gets doubled what happens to resistance? 80 times >> doubled >> 16 times >> doubled >> two power four >> 2 are four >> one more two two pairs of twos 2 2's are four 2 are four four are 16. So if radius doubles let's test becomes >> huh 16 1 by 16 * >> I'll tell you how see I told you that resistance I told you that resistance is inversely proportional to what is that R power 4 so previously you have taken a wire in which radius is R okay you have taken one more wire okay whose radius see this is R1 is R2 is 2 R or not So what I have done you know in this case I have taken a wire I have melted that wire the long wire I have melted and made it short when you made it short length decreases area increases that's it so this was a a very long wire I have made it short by just melting and radius has become doubled now so when r1= r2= 2 r so r2 by r1 is equal to R1 by R2 power 4. So therefore R2 by R1 is equal to R1 is R R2 is 2 R is going to be four * then this is going to be 2 by R1 is equal to 1 by 16. So therefore R2 will become R1 by 16. So this is going to be your new formula. Is it understood?

[00:12:41]In such cases if radius becomes doubles, resistance becomes 1x 16 times. If radius becomes half, distance becomes >> 16 times.

[00:12:56]>> Yeah. 1x 16 there 16 into I'll do that also. See see previously this was the radius R1= R. Now you have you have stretched it. R2 has become Rx2.

[00:13:12]Stretched means length increases, radius decreases. I told you that R is inversely proportional to R power 4 in stretching cases. Okay. So therefore R2 by R1 is equal to R1 by R2 power 4. So therefore R2 by R1 is equal to R1 by R2.

[00:13:29]R1 is how much? R2 is how much? RX2 whole power 4 getting cancelled. So 2 comes to the numerator. R2 by R1 is equal to 16. Therefore, R2 is equal to 16* of R1. Hope you understand what I'm saying. Is it clear? So, stretching cases he may not say stretching. Sometimes he may say a wire is taken it has been melted and drawn into a thin wire whose length is double drawn.

[00:14:02]If you don't use the word stretch, he said drawn.

[00:14:05]Hope you're understanding. So this is one basic concept. What is the next basic concept which is present in this?

[00:14:12]The next basic concept is let us take one small concept here. I have taken a wire of length L1 which is equal to okay 1 m and temperature P1 is equal how much? 0°C.

[00:14:25]Okay. So I have heated this wire to how much? 100°C.

[00:14:32]Length has become L2.

[00:14:35]length has raised to L2 and I have taken this one and the extra length after heating see whatever the item you heat whatever the broad whatever the body like metal you heat when you heat it expands metal you heat metal expands there are few things which does not expand which will contract after heating what is that thermal you heat it contracts plastic you heat it contract Foam you heat it contracts. So plastic materials will contract after heating whereas metals will expand on heating.

[00:15:16]The best example given in your IP material between the two rails gap is left. Why gap is left?

[00:15:23]So that insects will pass through that.

[00:15:27]The gap is left in summer it may expand and it may touch. In winter if there is no gap in summer in winter only it is touching each other. In summer what happens? It will expand. It will raise like this. So there will be speed breakers in the hat also. So gap is left through that. In summer it expands and some gap is less. Gap will be filled in summer. Every item expands on heat.

[00:15:53]Okay. So here also 1 m rod if you eat it increases its length to 1 mm. Huh. Okay.

[00:16:00]So what is what do you understand from this? You will understand from this that increase in the length is directly proportional to actual length. How do you say this one? I have taken one more example. I'll take one more example here. So instead of 1 m rod I am taking L1 equal to 2 m and I'm heating that rod. So previously this temperature was 0°C. Now the temperature is going to be 100°C. So now this is increasing its length to >> 1 m rod. If you heat to 100°C 1 mm is increased. 2 m rod if you need to heat to 100°C 2 mm is increased. What do you understand from this? You will understand from this that increase in the length is directly proportional to actual length. Increase in the length depends upon the actual length. Okay.

[00:16:49]For example, you have heated the same rod to 200°C then increase in the length becomes 2 mm. So one more relation you're getting increase in the length is directly proportional to rise in temperature.

[00:17:04]Increase in the length is directly proportional to length. Increase in the length is directly proportional to increase in temperature. If you join these two you will get a new relation.

[00:17:15]Okay? You're going to get a new relation. What is the new relation? L2 minus L1 is directly proportional to L1 into TS21.

[00:17:25]So when you remove this proportionality when you remove this proportionality you get L2 - L1 is equal to alpha into L1 into T2 -1. So from this it is understood that it is understood that alpha is equal to L2 - L1 by L1 into T2US.

[00:17:44]Okay. So this also written as co what is this alpha? Coefficient of expansion which is present in the heat chart.

[00:17:52]which is present in the heat chart where alpha is equal how much increase in the length by actual length into rise in temperature. Delta L is nothing but L2us L1 L is nothing but original length. T2 - T1 is written as why are you explaining that heat chapter here I'm explaining the heat chapter here because resistance is directly proportional to length.

[00:18:16]I'm just replacing length with resistance. So I'm just writing this formula. I'm just writing this formula which is present in heat chapter that is expansion of solids, liquids and gases.

[00:18:30]There is one chapter called as heat expansion of solids, liquids and gases.

[00:18:34]I'm just replacing this alpha as >> R2 - R1 by R1 into hope you're understanding. So based on this there are many problems in previous questions. You can just see sometime he now just I've solved one problem just now I have solved that ask for doubt here I have asked I have solved that problem he's telling that R2 is equal how much 8.6 >> 8.6 6 ohms it is given R1 is equal to 2 ohms it is given temperature P1 is 0 it's given temperature P2 is 80° this type of previous questions are asked so this resistances values they have been given I think first question yes sir >> first question in that material material this is some other question in your previous question okay so anyhow now after giving these values he's asking alpha take these values sub also hope you understand what I'm saying okay so if you understand this one if you understand this one then let us understand what happens in resistance in series resistance in parallel okay resistance in series see I have taken one resistance and another resistance both are connected in series and this is the potential difference so what is this resistance now this is R1 and this is R2 This potential which is present here gets divided here. This is V_sub_1 and this is V_sub_2. Okay. And as there is only one series one wire here the same current flows.

[00:20:15]Here potential gets divided but current is same. What is the condition here?

[00:20:20]This is the case of series connection in which I is same whereas V is divided.

[00:20:29]That is what we write.

[00:20:32]Then you write V= V1 + V_sub_2 and according to Ohm's law V= I V_sub1= I1 V_sub_2= I2 I same because there is connection there is no other way for current to go. It has to pass through a single wire. So here V means I write R series. Okay. V series is nothing but R I into R series and this is I into R1 plus I into R2. So I I I gets cancel. So R series is going to become R1 + R2. If one more resistance is added which is R3 then you get R series is going to be R1 + R2 + R3. The basic concept here. Now one resistance is here another resistance is connected in paral this is R1 this is R2 and they are being connected to a single potential that is V. So what do you understand from this here as this par connection this resistance is separately connected to this voltage that resistance is also separately connected to the same potential. So you understand that in this case also potential is V. In this case also potential is V. But here current is I1. Here current is I2. Here current is I. The same current comes up to here and here there are two ways. So some of the current will pass through here. Some of the current is passing through here. So in a par connection what is the condition in the par connection? V is same I is divided. In the previous case if you observe I is same B is divided. The next thing happens here. I is divided V is same. So whatever it is divided you should write I in parallel is going to be I1 + I2.

[00:22:18]Okay as V is same you can't add V. What is divided that is going to be added here in the previous case potential is divided. So potential is added how can you add I is only one. So here that is same and you all know according to Ohm's law V= I= V by R par I1 is equal to V by R1 I2 is equal to V by R2 just add them V by R par is equal to V by R1 + V by R2 so therefore what are you going to understand from this V if you come out and cancel R par is equal to 1x R1 R1 + 1 by R2. If one more par connection is given which is taken as R3 which is taken as R3 what are we going to get from this? Is it >> still get extra extra you get? What is that? 1x r= 1x r1 + 1x r2 + 1x r3. So here R par you just take LCM 1x R par is equal to R1 R2 is the product of the LCM is going to be the product and here we get R1 + R2. Therefore R par is nothing but R1 R2 by R1 + R2 isn't it? So here is the three cases. So 1x R par is going to be LCM is going to be just the product R1 R2 R3. So R1 if you common what is left R1 R3 is left. Okay. So you can write here R1 R2 plus R2 R3 in order I'm writing plus R3 R1 you are getting is it okay so R par is going to be if three combinations are there what do you write R1 R2 >> R3 >> plus R2 R3 >> plus R3 R4 >> so this is The shortcut formula for par connection when there are two R1 R2 by R1 + R2 when there are three R1 R2 R3 by R1 R2 R2 R3 R3 R1 isn't it?

[00:24:33]Next for example this type of resistances are there where here one resistance is there, here one resistance is there, here one resistance is there, here one resistance is there, here one resistance is there and let us imagine all are same. What is that? This is R.

[00:24:54]This is R.

[00:24:59]Okay. So, this is R. This is R. This is R. This is R. This is R. What are going to be parallel and what are going to be series? So, these two R series that's going to be 2 R. And this is par with R. So, 2 R into R by 2 R + R is going to be 2 R² by 3 R. So, getting cancel. So you're getting 2 RX 3 here.

[00:25:22]So what is the upper parts? It is going to be 2 RX 3 and this 2 RX 3 is connected to 1 R and this connected to one more R. Now series connection mean you just add them you write R + 2 RX 3 + R that is going to be A. This is going to be B. I'm asking what is R A B. So you just can add the answer. No. So what is going to be the answer? So 3 R + 2 R + 3 R / 3. So it's going to be how much?

[00:25:57]>> R 10 R by 10 R by 3 or 8 R 3.

[00:26:03]>> 8 R by 3 isn't it? Okay.

[00:26:07]And uh regularly one more type of question is asked many a times it has been answered.

[00:26:16]H yes see like this the diagram is present and here it is connected to a potential okay so what are the things you are going to see here there is a resistance R here there is resistance R here there is resistance R this is two times asked in the previous year questions and he's asking us to find out what is the current passing through this Okay. The formula is I is equal to V by RX. Single voltage is there but current resistances are many resistances are many. So from this you'll understand that these two are in series and these two are in par with this. So when two R series and par with this so this upper part is going to become 2 R and it is par with this R. So 2 R into R by 2 R + R is nothing but 2 R² by 3 R. getting cancelled. So I is going to be V by R which is nothing but 2 RX 3. So 3 V by 2 R is going to be your answer H. What is given? The values are given here something.

[00:27:29]See 77 question number it is given 333.

[00:27:33]So here also in the question itself it says that this is 3 volt. This is this is 3 ohms. This is 3 ohms. This is 3 ohms.

[00:27:44]Means what is that resistance? R means how much here? Three. You just substitute three here. So 3 V by 2 3 2 into 3 because R net is how much? R net is how much? Here 2 RX 3. No where R is 3 here.

[00:28:02]So 2 RX 3 means 2 into 3x3 will cancel 2 is left. Ret means how much? 2. So 3x2 is the answer.

[00:28:18]next one.

[00:28:21]C a triangular shape here.

[00:28:28]Potential what is the value of the potential? Is it is it given?

[00:28:33]>> 2 H 2 V.

[00:28:35]>> Yes. Okay. Net potential is 2 V.

[00:28:39]Okay. So net potential here is to be here there is resistance how much it is >> 3 ohms here 3 ohms here 3 ohms so these two are in series so 6 ohms okay and this 6 ohms is in par with 3 so 6 into 3 by 6 + 3 is nothing but 18 by 9 2 ohms is your answer or not so what is R here 2 ohms so I is equal to V net by R so I is equal what is Vet to be 2 V 2 V 2 W so 2 W so V net is nothing but 2 volt and R is nothing but two so your answer is one one ampere isn't it and one more here he has asked like this he has taken a triangle okay and he has taken this resistance this resistance and this resistance I think this is 6 ohms and 6 ohms and this is 3 ohms right I or Yes sir.

[00:29:40]>> Same.

[00:29:40]>> Yes sir.

[00:29:41]>> Or something else.

[00:29:42]>> Same.

[00:29:42]>> Same. And here they are connected to potential. What is the potential given?

[00:29:48]>> 4.8 volt.

[00:29:50]>> 4 volt.

[00:29:51]>> 8 volt. Isn't it? No. So you have to find out the current in this case. Am I right? Correct. You have to find out.

[00:29:57]Yes. Current you have to find out. That means I is nothing but V by R. R. How will you find out here? 6 + 6 is how much? 12. So this combination is 12 and 12 is in par with 3. Is it correct? So what do you write now? 12 into 3x 12 + 3. Okay. So 12 into 3 by 12 + 3. 12 into 3 you write like that only and this is going to be 15. All right. So 3 1 3 5.

[00:30:24]So what is R net? R is 12 by 5 and this is how much? 4.8 >> divided by R net which is how much?

[00:30:34]which is 12 by 5. So that is 12 on 1 12 4 * 5 4 are 20 R net is going to be 2 ohms 2 I'm sorry R is final sorry I find this is going to be I know I is nothing but V R is how much 4.8 R net is how much?

[00:30:59]>> 12 >> 12 x 5. So I is equal to V by R.

[00:31:05]I is equal to V by R. Vet is how much?

[00:31:09]4.8. Ret how much you are given?

[00:31:14]>> 12 by 5. So 12 / 5 means 4.8 into 5 by 12. 121 12 4 0.4. So 4 5 is 20. So 20 point here. So answer is how much? H2 and yes.

[00:31:26]>> Is it okay? Yes. Shall we stop?