Question

The resistors each of resistance 1 ohm is connected as shown in the figure. The resultant resistance between A and B is :
a) 11/5. b) 5/11. c) 6/5. d) 5/6


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Answer 1

Explanation:

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Answer 2

The resultant resistance is $\dfrac{5}{11}$

(b) is correct option.

Explanation:

Given that,

The resistors each of resistance = 1 ohm

$R_{1}$ and $R_{2}$ in parallel

We need to calculate the  resistance

Using parallel formula of resistance

$\dfrac{1}{R}=\dfrac{1}{R_{1}}+\dfrac{1}{R_{2}}$

$\dfrac{1}{R}=\dfrac{1}{1}+\dfrac{1}{1}$

$R=\dfrac{1}{2}\ \Omega$

$R_{3}$, $R_{4}$ and $R_{5}$ in parallel

We need to calculate the resistance

Using parallel formula of resistance

$\dfrac{1}{R'}=\dfrac{1}{R_{3}}+\dfrac{1}{R_{4}}+\dfrac{1}{R_{5}}$

$\dfrac{1}{R'}=\dfrac{1}{1}+\dfrac{1}{1}+\dfrac{1}{1}$

$R'=\dfrac{1}{3}\ \Omega$

Now, R and R' in series

We need to calculate the resistance

Now, R and R' in series

$R''=R+R'$

$R''=\dfrac{1}{2}+\dfrac{1}{3}$

$R''=\dfrac{5}{6}$

Now, R'' and $R_{6}$ in parallel

We need to calculate the resultant resistance

Using formula of parallel resistance

$\dfrac{1}{R'''}=\dfrac{1}{R''}+\dfrac{1}{R_{6}}$

Put the value into the formula

$\dfrac{1}{R'''}=\dfrac{6}{5}+\dfrac{1}{1}$

$R'''=\dfrac{5}{11}$

Hence, The resultant resistance is $\dfrac{5}{11}$

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Topic : resultant resistance

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