Question

Three resistors R1 ohm, 4ohm and 8 ohm are connected series circuit . If the resultant resistance is 20ohms . Find the value of R1 .

Answer 1

Given :-

Three resistors are connected in a series

$\sf \bullet R_1= ?\\ \\ \sf \bullet R_2= 4\ \Omega \\ \\ \sf\bullet R_3= 8 \Omega\\ \\ \sf \bullet Resultant \ resistance(R_s) = 20 \Omega$

To find

$\sf \star R_1 = ?$

◆We know that resistance in series

$\boxed{\sf{R_s= R_1+R_2+R_3.\ ..\ ... +R_n}}$

here ,

$\sf R_s =$ The sum of their individual resistance.

Now put the given values !

$\longmapsto\sf 20 \Omega=R_1+ 4\Omega+ 8\Omega \\ \\ \longmapsto\sf 20\Omega = R_1+12\Omega\\ \\ \longmapsto\sf 20\Omega-12\Omega= R_1\\ \\ \longmapsto\sf 8\Omega= R_1\\ \\ \longmapsto\sf \ \ or \ R_1= 8\Omega$

$\bigstar{\boxed{\sf{R_1= 8\Omega}}}$

Resistance in parallel

$\boxed{\sf{\dfrac{1}{R_p}= \dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}....\ ..\ .. +\dfrac{1}{R_n}}}$

Answer 2

$\huge{\underline{\underline {\bf{\red{\ Answer:-}}}}}$

★ $\large\bold{\underline{\underline{\sf{\pink{GivEn:-}}}}}$

$\implies$ Three resistors connected in series:-

$\ \ \ \ \ \ \ \ \ \bullet \sf R_1 → \ ?$

$\ \ \ \ \ \ \ \ \ \bullet \sf R_2 → \ 4 \Omega$

$\ \ \ \ \ \ \ \ \ \bullet \sf R_1 → \ 8 \Omega$

$\ \ \ \ \ \ \ \ \ \bullet$ resultant resistor $\sf R_s → \ 20 \Omega$

★ $\large\bold{\underline{\underline{\sf{\pink{To \; Find:-}}}}}$

$\implies \sf R_1 = ?$

★ Now, Putting all values in formula:-

$\large\bold{\underline{\boxed{\sf{\purple{ \sf R_s → \sf R_1 + \sf R_2 + \sf R_3..... \sf R_n }}}}}$

★ $\large\bold{\underline{\underline{\sf{\pink{20 \Omega → \sf R_1 + 4 \Omega + 8 \Omega}}}}}$

$\implies 20 \Omega → \sf R_1 \Omega + 12 \Omega$

$\implies 20 \Omega - 12 \Omega → \sf R_1 \Omega$

$\implies \large\bold{\underline{\boxed{\sf{\red{\dag \; 8 \Omega \; → \; \sf R_1 }}}}}$

★ Related Formula :-

$\implies$ Resistance in Parallel:-

$\large\bold{\underline{\boxed{\sf{\purple{\dfrac{1}{ \sf R_p} → \dfrac{1}{ \sf R_1} + \dfrac{1}{ \sf R_2} + \dfrac{1}{ \sf R_3}....... \dfrac{1}{\sf R_n }}}}}}$

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