In a circuit 10 ohm is connected in series and 20 and 20 ohm is connected in parallel find the equivalent resistance
Answers
Thanks for the A2A. I really appreciate your query. This question is very easy to answer if you the basic concept of “Resistors”.
As we all know that Resistors can be connected in series or in parallel connection.
When resistors are connected in series, then the equivalent resistance of all series connected resistors will be the sum of all individual resistors. We have to just simply add those individual resistors.
R1 + R2 + R3 … + Rn = Req (In series connection)
Similarly,
When resistors are connected in parallel, then the equivalent resistance of all parallel connected resistors will be the lowest value of all individual resistors values. We have to just simply divide those individual resistors.
1/R1 + 1/R2 + 1/R3 … + 1/Rn = 1/Req (In series connection)
Please check the attached images.
The above explanation is very necessary to give you a basic idea, so for the next time, you will solve these types of questions by yourself instead of asking it here.
Now the actual question,
Resistors having a resistance of 15 ohms, 20 ohms. and 10 ohms are connected in parallel. What is the effective resistance in the circuit?
We know the basic formula, as I have defined above. Please use it.
1/R1 + 1/R2 + 1/R3 … + 1/Rn = 1/Req
Putting the values of R1, R2, R3
1/15 + 1/20 + 1/10 = 1/Req
Now, taking L.C.M of three
{1(20*10) + 1(15*10) + 1(15*20)}/15*20*10 = 1/Req
(200 + 150 + 300)/3000 = 1/Req
650/3000 = 1/Req
13/60 = 1/Req
Cross Multiply
13*Req = 1*60
13*Req = 60
Req = 60/13
Req = 4.615 ohms
See first we calculate for the parallel !! So :-
1/Rp = 1/20+1/20 = 2/20
Rp = 20/2= 10ohm !
Thus the equivalent resistance for parallel connection is 10ohms
Therefore the total will b Rs+Rp :-
There is only one resistor as a series connection to it ..
Therefore the answer is :-
10 + 10 = 20 ohms is the equivalent resistance of the whole circuit !!
So easy my love ..
