Question

The equivalent resistance when two resistors are connected in series and parallel are 10 ohm and 1.6 ohm
The value of the individual resistance is
0
6 and 4 ohm
0
7 and 3 ohm
O Band 2 ohm
o
9 and 1ohm​

Answer 1

▶ The equivalent resistance when two resistors are connected in series and parallel are 10Ω and 1.6Ω.

▶ We have to find the individual resistance of each resistor.

Series Connection :

▪ Formula of equivalent resistance in series connection is given by

$\boxed{\bf{\pink{R_s=R_1+R_2}}}$

Parallel Connection :

▪ Formula of equivalent resistance in parallel connection is given by

$\boxed{\bf{\purple{\dfrac{1}{R_p}=\dfrac{1}{R_1}+\dfrac{1}{R_2}}}}$

Calculation :

$\rightarrow\sf\:R_1+R_2=10.....(1)\\ \\ \rightarrow\sf\:1.6=\dfrac{R_1R_2}{R_1+R_2}\\ \\ \rightarrow\sf\:R_1R_2=10\times 1.6\\ \\ \rightarrow\sf\:R_1R_2=16.....(2)\\ \\ \dag\sf\blue{from\:(1)\:and\:(2)}\\ \\ \rightarrow\sf\:R_1+\dfrac{16}{R_1}=10\\ \\ \rightarrow\sf\:{R_1}^2+16=10R_1\\ \\ \rightarrow\sf\:{R_1}^2-10R_1+16=0\\ \\ \rightarrow\sf\:{R_1}^2-8R_1-2R_1+16=0\\ \\ \rightarrow\sf\:R_1(R_1-8)-2(R_1-8)=0\\ \\ \rightarrow\bf\:R_1=2\Omega\:or\:R_1=8\Omega\\ \\ \rightarrow\bf\:R_2=8\Omega\:or\:R_2=2\Omega$