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

2 Ω

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1 Ω

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1.5 Ω

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3 Ω

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Solution

The correct option is B $1 Ω$
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 $\frac{1}{12} + \frac{1}{x + 5} = \frac{1}{4} a s t h e t o t a l r e s i s t a n c e i s g i v e n a s 4 o h m s i n t h e q u e s t i o n .$
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.

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

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