Question

When two resistors are connected in series and parallel then their equivalent resistance are 16 ohm 3 ohm respectively find out the resistance of its?

Answer 1

Answer:

12 & 4 ohms

Explanation:

let, the resistances are a & b

so, a+b = 16

and   a^(-1) + b^(-1) =3^(-1)

or, (a+b)/ab=3^(-1)

or,16/ab=3^(-1)

or, ab=48

or,(a-b)^2=(a+b)^2-4ab=16^2-4*48=64

or,a-b=8

so, a= 12, b= 4  

Answer 2

The value of two resistances is 4 and 12 ohms.

Explanation:

Given that,

Let $R_1\ and\ R_2$ is the two resistors. When they are connected in series their equivalent resistance of resistors is given by :

$R_s=R_1+R_2$

$16=R_1+R_2$.......(1)

When they are connected in parallel their equivalent resistance of resistors is given by :

$\dfrac{1}{R_p}=\dfrac{1}{R_1}+\dfrac{1}{R_2}$

$\dfrac{1}{3}=\dfrac{1}{R_1}+\dfrac{1}{R_2}$..............(2)

On solving equation (1) and (2) we get :

$R_1=4\ \Omega\\R_2=12\ \Omega$

So, the value of two resistances is 4 and 12 ohms.

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