Question

11. What is the value of r in the following
network? The effective resistance of the
network between PQ is 1 12. (Ans. 22)​

Answer 1

Correct Question :

what is the value of r in the following network. The effective resistance of the network between PQ is 1Ω

$\rule{200}2$

Before solving the question , Let's know about some Combination of resistors .

• Resistors in series and parallel :

1) Resistors in series :

For n resistors connected in series

the equivalent Resistance $R_{eq}$ is given by

$R_{eq}=R_{1}+R_{2}+R_{3}+...+R_{4}$

2) Resistors in parallel:

For n resistors connected in parallel

the equivalent Resistance $R_{eq}$ is given by

$\dfrac{1}{R_{eq}} = \dfrac{1}{R_{1} } + \dfrac{1}{R_{2} } + \dfrac{1}{R_{3} } + ...... \dfrac{1}{R_{n} }$

Solution :

We have to find the vale of r

$\sf\:R_{eq}=\dfrac{2r}{2+r}$

$\implies\sf\:1=\dfrac{2r}{2+r}$

$\sf\implies2+r=2r$

$\implies\sf\:2r-r=2$

$\implies\sf\:r=2$Ω

Therefore, The vale of r is 2Ω

Note :

For. step by step explanation refer to the attachment .

Answer 2

Answer:

Correct Question :

what is the value of r in the following network. The effective resistance of the network between PQ is 1Ω

\rule{200}2

Before solving the question , Let's know about some Combination of resistors .

• Resistors in series and parallel :

1) Resistors in series :

For n resistors connected in series

the equivalent Resistance R_{eq}R

eq

is given by

R_{eq}=R_{1}+R_{2}+R_{3}+...+R_{4}R

eq

=R

1

+R

2

+R

3

+...+R

4

2) Resistors in parallel:

For n resistors connected in parallel

the equivalent Resistance R_{eq}R

eq

is given by

\dfrac{1}{R_{eq}} = \dfrac{1}{R_{1} } + \dfrac{1}{R_{2} } + \dfrac{1}{R_{3} } + ...... \dfrac{1}{R_{n} }

R

eq

1

=

R

1

1

+

R

2

1

+

R

3

1

+......

R

n

1

Solution :

We have to find the vale of r

\sf\:R_{eq}=\dfrac{2r}{2+r}R

eq

=

2+r

2r

\implies\sf\:1=\dfrac{2r}{2+r}⟹1=

2+r

2r

\sf\implies2+r=2r⟹2+r=2r

\implies\sf\:2r-r=2⟹2r−r=2

\implies\sf\:r=2⟹r=2 Ω

Therefore, The vale of r is 2Ω

Note :

For. step by step explanation refer to the attachment .