Question

4.
What is the effective resistance between A and B
in the given network?
Plz help me.....​

Answer 1

Given

a circuit containing combination of resistances in both series and parallel combination.

Series Combination

• When resistances are arranged in such a fashion that the second resistances is connected to the end of first resistances, they are said to be in series combination.For examples :- All the 1 ohm resistances are in series here,Likewise 2 ohm and 3 ohm resistors are in series.

In this case , $R_{eq}\:=\:R_1\:+R_2\:+\:R_3$

Parallel Combination

• When resistances are connected across the same point,they are said to be in parallel combination

$\dfrac{1}{R_{eq}}\:=\: \dfrac{1}{R_1}\:+\: \dfrac{1}{R_2}\:$

Solutions

Here, 1 ohm resistors are in series,finding their equivalent R

R = 1 + 1 + 1 + 1 + 1

=> R = 5 ohm

Also, 2 ohm and 3 ohm resistors are series,finding their equivalent R'

R' = 2 + 3

=> R' = 5 ohm.

Now, R and R' would be in parallel ,finding their equivalent :-

$\dfrac{1}{R_{eq}}\:=\: \dfrac{1}{5}\:+\: \dfrac{1}{5} \\ \\ \\ => R_{eq}\:=\: \dfrac{5}{2} \\ \\ \\ =>\: R_{eq}\:=\:2.5\:ohm$.

Hence,the answer is 2.5 ohm.

Time saving Calculations

• Parallel combination of two equal resistances give a value of equal to their half.For example, in this question,we got 2.5 ohm.

• Parallel combination of 3 ohm and 6 ohm gives 2 ohm.