Question

How will u connect the three resistors 4ohm, 6ohm and 12ohm so that the resultant resistance is 9ohm. draw a diagram? Plz answer if u know since I am practicing for my test and got stuck with this question!

Answer 1

Answer:-

• Connect 4ohm and 12ohm resistor in parallel connection and 6ohm resistor in series connection together

$\LARGE{\fcolorbox{black}{white}{\color{black}{\bf Verification:-}}}$

• R1=4ohm
• R2=6ohm
• R3=12ohm

In parallel connection:-

$\boxed{\sf \dfrac{1}{R_{13}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}}$

$\\ \sf \longrightarrow \: \dfrac{1}{R_{13}}=\dfrac{1}{4}+\dfrac{1}{12}$

$\\ \sf \longrightarrow \: \dfrac{1}{R_{13}}=\dfrac{3+1}{12}$

$\\ \sf \longrightarrow \: \dfrac{1}{R_{13}}=\dfrac{4}{12}$

$\\ \sf \longrightarrow \: \dfrac{1}{R_{13}}=\dfrac{1}{3}$

$\\ \sf \longrightarrow \:R_{13}=3\Omega$

In series connection:-

$\boxed{\sf R_{123}=R_{13}+R_2}$

$\\ \sf \longrightarrow \:R_{123}=3+6$

$\\ \sf \longrightarrow \:R_{123}=9\Omega$

henceforth $\small{\fcolorbox{green}{green}{\color{white}{\bf Verified}}}$