Question

The resistors each of resistance 1 ohm is connected as shown in figure.
The resultant resistance between A and B is

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Answer 1

Answer:

O. 167ohms

Explanation:

The resistors are all arranged in parallel which are in series with the last resistor

Answer 2

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

Explanation:

Given that,

The resistors each of resistance =1 ohm

We need to calculate the resultant resistance

Using series and parallel formula of resistance

Resistance R₁ and R₂ in parallel

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

Put the value into the formula

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

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

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

Now, R₃, R₄ and R₅ in parallel

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

Put the value in to the

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

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

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

Now, R and R' in series

Using series formula

$R''=R+R'$

Put the value into the formula

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

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

Now, R'' and R₆ in parallel

Using parallel formula

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

Put the value into the formula

$\dfrac{1}{R_{r}}=\dfrac{6}{5}+\dfrac{1}{1}$

$R_{r}=\dfrac{5}{11}\ \Omega$

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

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Topic : resistance

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