Question

In the circuit shown below in Fig., the value of x if the equivalent resistance between A and B is $4\Omega$ will be:

• A. $2\Omega$
• B. $1\Omega$
• C. $1.5\Omega$
• D. $3\Omega$

Answer 1

Answer: (B)

In this case, the 2 resistors of 4 ohms and 8 ohms are connected in series and the combined resistance is given as 4+8 = 12 ohms.
The 2 resistors of x ohms and 5 ohms are connected in series and the combined resistance is given as x+5 ohms.
The above 2 sets of resistors are connected in parallel. Thus, the total resistance is expressed as $\frac{1}{12}+\frac{1}{x+5}=\frac{1}{4}asthetotalresistanceisgivenas4ohmsinthequestion.$
Solving for x in the above equation we get x=0.99. That is. 1 ohm approximately.
Hence, the value of the unknown resistance in the circuit is 1 ohm.