Question

Supposing three resistors of magnitude 2ohms, R and 3ohms respectively,are connected in series .Find the value of R in ohms if the equivalent resistors is expected to be 15ohms

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Value\:of\:R=10\Omega}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Resistors = 2 \Omega , \: R, \: 3\Omega \\ \\ \tt: \implies R_{equivalent} = 15\Omega \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Value \: of \: R= ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies R_{equivalent} = R_{1} + R_{2} + R_{3} \\ \\ \tt: \implies 15 = 2 + R + 3 \\ \\ \tt: \implies 15 = 5 + R \\ \\ \tt: \implies R= 15 - 5 \\ \\ \green{\tt: \implies R= 10\Omega} \\ \\ \blue{\bold{Some \: related \: formula}} \\ \\ \red{\text{For \: parrallel \: series}}\\ \orange{\tt \circ \: R_{equivalent} = \frac{1}{ R_{1} } + \frac{1}{ R_{2} } + \frac{1}{ R_{3} } + .... + \frac{1}{ R_{n} } } \\ \\ \orange {\tt \circ \: V= IR}$

Answer 2

$\tt{\huge{\orange{Hello!!! }}} B.Q.$

QUESTION :

Supposing three resistors of magnitude 2ohms, R and 3ohms respectively,are connected in series .

Find the value of R in ohms if the equivalent resistors is expected to be 15ohms.

SOLUTION :

$\tt{\leadsto{\red{Given \::- }}} \\ \\ \tt{\mapsto{\green{R_{1} = 2 \: \Ohm }}} \\ \\ \tt{\mapsto{\green{R_{2} = 3 \: \Ohm }}} \\ \\ \tt{\mapsto{\green{R_{3} = R \: \Ohm }}}$

We know that for Resistances in series,

$\tt{\blue{\mapsto{R_{eq} = R_{1} + R_{2} + ...... }}}$

Hence in this case :

2 Ohm + 3 Ohm + R ohm = 15 Ohm

=> R ohm = 15 Ohm - 5 Ohm = 10 Ohm .

So the value of R is 10 Ohms ..........(A)