Two known resistances of R and 2R and one unknown resistance X are connected in a circuit as shown in the figure. If the equivalent resistance between points A and B in the circuit is X , then the value of X is . [figure]
- 2( 3 - 1)R
- R
- ( 3 - 1)R
- ( 3 + 1)R
Answer
(3) ( 3 - 1)R
Solution
2R and X are in series; this combination is in parallel with R.
RAB = (2R + X)R(2R + X) + R = X
2R2 + XR = 3RX + X2
X2 + 2RX - 2R2 = 0
X = -2R + 4R2 + 8R22 = ( 3 - 1)R (X > 0)
Answer: (3)