Why equivalent resistance increases. in series but decreases in parrellel combinations
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Answers
Answer :
Question is why equivalent resistance in series increases but decreases in parallel combination?
First of all I would clear the concept of equivalent resistance in a circuit.
★ In series all the resistors are on the same line and current passes only in that line. So the equivalent resistance in a series increases as all the resistors are added.
★ In parallel , reciprocals of all resistors are added and current gets many paths to flow, so the equivalent resistance in a parallel combination decreases .
★ In a parallel combination, equivalent resistance < Smallest resistor.
Now why difference in equivalent resistances of both combinations occurs?
Reason is that when current has only one way to flow in series then it increases the equivalent resistance . But when current has multiple ways to flow then it actually decreases the equivalent resistance in parallel.
Example :
If we take 3 resistors of equal resistances of 5Ω are connected in series and parallel , which equivalent resistance will be smaller or which will be bigger?
As we know that,
R(S) = R1 + R2 + R3 + ................
→ R(S) = 5 + 5 + 5
→ R(S) = 15Ω
Therefore, equivalent resistance in series = 15Ω
Again,
We know that,
1/R(P) = 1/R1 + 1/R2 + 1/R3 + ...........
→ 1/R(P) = 1/5 + 1/5 + 1/5
→ 1/R(P) = (1 + 1 + 1)/5
→ 1/R(P) = 3/5
→ 3R (P) = 5
→ R(P) = 5/3
→ R(P) = 1.67Ω
Therefore, equivalent resistance in parallel = 1.67Ω
Now we can see that, equivalent resistance in series > Equivalent resistance in parallel.
Hence we can now say that it increases or decreases because of current flowing & reciprocals of resistance are added in parallel and direct value of resistances are added in series.
Answer:
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