Question

A circuit having resistance R1 = 2 ohm and R2 = 3 ohm.Find the total resistance if they are
i ) in series
ii ) in parallel..
​

Answer 1

Given :

▪ Two identical resiators of resistances 2Ω and 3Ω are connected in

• Series
• Parallel

To Find :

→ Equivalent resistance in each case.

Formula :

◐ Eq. resistance for series connection :

$\bigstar\:\underline{\boxed{\bf{\red{R_s=R_1+R_2+...+R_n}}}}$

◐ Eq. resistance for parallel connection :

$\bigstar\:\underline{\boxed{\bf{\blue{\dfrac{1}{R_p}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+...+\dfrac{1}{R_n}}}}}$

Calculation :

❇ Case - I :

$\implies\sf\:R_s=R_1+R_2\\ \\ \implies\sf\:R_s=2+3\\ \\ \implies\underline{\boxed{\bf{\green{R_s=5\Omega}}}}\:\orange{\bigstar}$

❇ Case - II :

$\mapsto\sf\:\dfrac{1}{R_p}=\dfrac{1}{R_1}+\dfrac{1}{R_2}\\ \\ \mapsto\sf\:\dfrac{1}{R_p}=\dfrac{1}{2}+\dfrac{1}{3}\\ \\ \mapsto\sf\:R_p=\dfrac{2\times 3}{2+3}=\dfrac{6}{5}\\ \\ \mapsto\underline{\boxed{\bf{\gray{R_p=1.2\Omega}}}}\:\orange{\bigstar}$

Answer 2

Given R1 = 2 Ω , R2 = 3Ω

$\bold{When\;resistances\;are\;connected\;in\;series}\\\\ \bold{\bf{\blue{R_s=R_1+R_2+R_3+...}}}\\\\\bold{When\;resistances\;are\;connected\;in\;parallel}\\\\\bold{\bf{\red{\frac{1}{R_p}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+... }}}$

( i )

$\bold{R_s=R_1+R_2}\\\\\implies \bold{R_s=2+3}\\\\\implies \bold{\bf{\red{R_s=5\;\Omega}}}$

( ii )

$\bold{\frac{1}{R_p}=\frac{1}{R_1} +\frac{1}{R_2} }\\\\\implies \bold{\frac{1}{R_p}=\frac{1}{2}+\frac{1}{3} }\\\\\implies \bold{\bf{\blue{R_p=1.2\;\Omega}}}$