Question

How would you connect three resistors each of resistance 8 ohm so that the

combination has resistance a) 12 ohm b) 5.3 ohm​

Answer 1

Answer :-

a) 12 ohm

For 12 ohm we will connect firstly two resistors in parallel and the combination of these resistors in series with the third resistor

• Firstly two resistors in parallel

$\implies\sf{\dfrac{1}{\ R_{p}}=\dfrac{1}{8}+\dfrac{1}{8}}$

$\implies\sf{\ R_{p}=\dfrac{8\times 8}{8+8}}$

$\implies\sf{\ R_{p}=\dfrac{64}{16}}$

$\implies\sf{\ R_{p}=\dfrac{\cancel{64}}{\cancel{16}}}$

$\implies\sf{\ R_{p}=4\:ohm}$

• Now in series with third resistor

$\implies\sf{\ R_{s}=4+8}$

$\implies\sf{\ R_{s}=12\:ohm}$

So , there is an equivalent resistance of 12 ohm

b) 5.3 ohm

For 5.3 ohm we will connect firstly two resistors in series and the combination of these resistors in parallel with the third resistor

• Firstly two resistors in series

$\implies\sf{\ R_{s}=8+8}$

$\implies\sf{\ R_{s}=16\:ohm}$

• Now connect this resultant with the III resistor in parallel

$\implies\sf{\dfrac{1}{\ R_{p}}=\dfrac{1}{16}+\dfrac{1}{8}}$

$\implies\sf{\ R_{p}=\dfrac{16\times 8}{16+8}}$

$\implies\sf{\ R_{p}=\dfrac{128}{24}}$

$\implies\sf{\ R_{p}=5.3\:ohm}$

So , there is an equivalent resistance of 5.3 ohm