Question

CALCULATE THE EQUIVALENT RESISTANCE OF POINTS A AND B

Answer 1

$\large\underline{\bigstar \: \: {\sf To \: Find-}}$

Equivalent Resistance between point A and B

$\large\underline{\bigstar \: \: {\sf Solution-}}$

We know that -

➩ Series Combination

$\implies\underline{\boxed{\sf R_{eq}=R_1+R_2+R_2....so \; on }}$

➩ Parallel Combination

$\implies\underline{\boxed{\sf \dfrac{1}{R_{eq}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}...\;so \: on}}$

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★ 6Ω and 6Ω are in Parallel Combination :

$\implies{\sf \dfrac{1}{R'}=\dfrac{1}{6}+\dfrac{1}{6} }$

$\implies{\sf \dfrac{1}{R'}=\dfrac{2}{6} }$

$\implies{\sf R'=\dfrac{6}{2} }$

$\implies{\rm R'=3\ohm}$

★ 6Ω and 6Ω are in Parallel Combination :

$\implies{\sf \dfrac{1}{R"}=\dfrac{1}{6}+\dfrac{1}{6} }$

$\implies{\sf \dfrac{1}{R"}=\dfrac{2}{6} }$

$\implies{\sf R"=\dfrac{6}{2}}$

$\implies{\rm R"=3\ohm }$

★ Now R' and R" are in Series Combination :

$\implies{\sf R_{eq}=R'+R"}$

$\implies{\sf R_{eq}=3+3 }$

$\implies{\bf R_{eq}=6\ohm }$

$\large\underline{\bigstar \: \: {\sf Answer-}}$

Equivalent Resistance between A and B is ${\bf 6\ohm}$

Answer 2

We know that ,

The equivalent resistance in parrallel combination is given by

$\large \mathbb{ \fbox{ \frac{1}{R} = \frac{1}{ R_{ \sf{1}}} + \frac{1}{ R_{ \sf{2}}} + ... + \frac{1}{ R_{ \sf{n}}} }}$

The equivalent resistance in parrallel combination is given by

$\mathbb{ \large\fbox{R = R_{ \sf{1}} + R_{ \sf{2}} + ... + R_{ \sf{n}}}}$

Clearly, 6 Ω and 6 Ω are in parrallel

Thus ,

Their equivalent resistance is

1/R = 1/6 + 1/6

1/R = 2/6

R = 6/2

R = 3 ohm

Also , 6 Ω and 6 Ω are in parrallel

Thus ,

1/R' = 1/6 + 1/6

1/R' = 1/6

R' = 6/2

R' = 3 ohm

Now , R and R' forms a series combination , so

R" = 3 + 3

R" = 6 ohm

Hence , the equivalent resistance b/w A and B is 6 ohm