Question

In the circuit shown below . calculate the value of x if the equivalent resistance between the point A and B is 4ohm​

Answer 1

Answer:

since the upper arm resistors are in series

R1=4+8 =12ohms

in lower arm

R2=x+5=(5+x) ohms

we know that

1/Rs=1/R1+1/R2. ( when resistors are in parallel combination)

Rs=4 ohms (given)

1/4=1/12+1/5+x

1/4-1/12=1/5+x

3-1/12=1/5+x

2/12=1/(5+x)

1/6=1/(5+x)

therefore on taking reciprocal

6=5+x

1=x

thus value of x is 1ohm

Answer 2

Answer:

the value of x is 1 Ω

Explanation:

Given,

Equivalent resistance between A and B is 4Ω.

in the given figure,

4Ω and 8Ω resistors are in series,

so, Req = ( 4 + 8)Ω = 12Ω

also, x Ω and 5Ω resistors are in series,

so, Req = (x + 5) Ω

and, now, 12 Ω and (x + 5) ohm resistors are in parallel.

then, 1/Req =1/12 + 1 / (x + 5)

or, 1 / 4 = 1 / 12 + 1 / (x + 5)

or, 1 / 4 = [(x+5) + 12] / 12(x+5)

or, 1 / 4 = (x + 17) / (12x + 60)

or, 12x + 60 = 4(x  + 17)

or, 12x + 60 = 4x + 68

or, 12x - 4x = 68 - 60

or, 8x = 8

or, x = 1 Ω

Therefore, the value of x is 1 Ω.