Question

Three unequal resistors in parallel are equivalent to a resistance 1 ohm. if two of them are in the ratio 1: 2 and if no resistance value is fractional, the largest of the three resistances in ohms is.

Answer 1

Let the three resistance be R1,R2,R3

Therefore the largest resistance it 6 ohm

Answer 2

Answer:

6 ohm

Explanation:

We are given that three unequal  resistance in parallel are their equivalent resistance is 1 ohm .We are also given that if two of them are in the ratio 1:2 and value of any resistance is not fractional

We have to find the value of largest of the three resistances in ohm

Let $R_1,R_2 and R_3$ are three unequal resistance

Let $R_1=k$

$R_2=2k$

When resistance are arranged in parallel then

Equivalent resistance=$\frac{1}{R} =\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$

Applying this formula

$1=\frac{1}{k}+\frac{1}{2k}+\frac{1}{R_3}$

$\frac{1}{R_3}=1-\frac{1}{k}-\frac{1}{2k}$

$\frac{1}{R_3}=\frac{2k-3}{2k}$

$R_3=\frac{2k}{2k-3}$ (By taking reciprocal )

If substitute k=1 then we get

$R_3=-2$ it is not possible because resistance can no be negative

When we take k=2

$R_3=4 ohm,R_1=2 ohm \;and \;R_2=4 ohm$

It is not possible because three resistor are unequal

When k=3 then we get

$R_3=\frac{2\times3 }{2\times3-3}=2 ohm$

$R_1= 3 ohm$ and $R_2=2\times 3=6 ohm$

Hence, the largest value of resistor is 6 ohm .