Question

find the equivalent resistance across the two ends a and b of the following circuit

Answer 1

Given that,

4 resistors of resistance 5 ohms each.

To find,

The equivalent resistance of the resistors.

Solution,

In the middle branch, two 5 ohms resistors are connected in series. Their equivalent is equal to :

$R_s=5+5\\\\R_s=10\ \Omega$

Now, resistor in the upper, middle and lower branch are connected in parallel. The equivalent resistance is given by :

$\dfrac{1}{R}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}\\\\\dfrac{1}{R}=\dfrac{1}{5}+\dfrac{1}{10}+\dfrac{1}{5}\\\\R=2\ \Omega$

So, the equivalent resistance is 2 ohms.