Question

Please help in finding the x ohm resistor

Answer 1

$\mathtt{\huge{ \fbox{Solution :)}}}$

Given ,

The equivalent resistance b/w A and B is 4 ohm

Clearly , 4 Ω and 8 Ω resistance are connected in series combination

Thus ,

R' = 4 + 8

R' = 12 ohm

Also , x Ω and 5 Ω resistance are connected in series combination

Thus ,

R" = (x + 5) Ω

Now , The resistance R' form a parrallel combination with R"

Thus , the equivalent resistance b/w A and B is

➡1/R = 1/12 + 1/(x + 5)

➡1/R = (x + 17)/(12x + 60)

➡R = (12x + 60)/(x + 17)

Since , the equivalent resistance b/w A and B is 4 Ω

Thus ,

$\sf \hookrightarrow 4 = \frac{12x + 60}{x + 17} \\ \\ \sf \hookrightarrow 4x + 68 = 12x + 60 \\ \\ \sf \hookrightarrow 8x= </p><p>8 \\ \\ \sf \hookrightarrow x = 1 \: \: ohm$

Hence , the value of x is 1 ohm