Find the equivalent resistance between A and B.

Question

Verified by Toppr

Answer 1

$Step 1 - Using parallel combination :$
$∵ 6 Ω$ and $3 Ω$ are in parallel.
So, their equivalent Resistance $R^{'} = \frac{6 Ω \times 3 Ω}{6 Ω + 3 Ω}$
$R^{'} = 2 Ω$
Also, $4 Ω$ and $12 Ω$ are in parallel
So, this equivalent Resistance $R^{''} = \frac{4 Ω \times 1 2 Ω}{4 Ω + 1 2 Ω}$
$R^{''} = \frac{4 8 Ω}{1 6} = 3 Ω$

$Step 2 - Using series combination :$
Simplified circuit becomes :-

$∵ R^{'}$ and $R^{''}$ are in series.
So, equivalent Resistance $R_{A B} = R^{'} + R^{''}$
$= 2 Ω + 3 Ω$
$= 5 Ω$

Therefore, equivalent Resistance between $A$ and $B$ is $5 Ω$

Answer 2

Step 1 - Using parallel combination :

∵ 6 Ω

and

3 Ω

are in parallel.

So, their equivalent Resistance

R^{'} = \frac{6 Ω \times 3 Ω}{6 Ω + 3 Ω}

R^{'} = 2 Ω

Also,

4 Ω

and

12 Ω

are in parallel

So, this equivalent Resistance

R^{''} = \frac{4 Ω \times 1 2 Ω}{4 Ω + 1 2 Ω}

R^{''} = \frac{4 8 Ω}{1 6} = 3 Ω

Step 2 - Using series combination :

Simplified circuit becomes :-

∵ R^{'}

and

R^{''}

are in series.

So, equivalent Resistance

R_{A B} = R^{'} + R^{''}

= 2 Ω + 3 Ω

= 5 Ω

Therefore, equivalent Resistance between

A

and

B

is

5 Ω