Question

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

Answer 1

Answer:

c)6/5 is correct answer.

Answer 2

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

(b) is correct option

Explanation:

Given that,

The resistors each of resistance 1 ohm.

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

We need to calculate the Resistance

Using formula of parallel

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

Put the value into the formula

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

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

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

We need to calculate the Resistance

Using formula of parallel

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

Put the value into the formula

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

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

Now, R and R' in series

We need to calculate the resistance

Using formula of resistance

$R''=R+R'$

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

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

Now, R'' and [/tex]R_{6}[/tex] in parallel

We need to calculate the resultant resistance

Using formula of parallel

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

Put the value into the formula

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

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

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

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Topic : resultant resistance

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