Question

Three resistors of resistance 5 Ω each are connected in series. The combined resistance will be equal to
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Answer 1

Resultant resistance is 15 Ω

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$\orange{\bigstar}$  Given  $\green{\bigstar}$

Three resistors of resistance 5 Ω each are connected in series

$\orange{\bigstar}$  To Find  $\green{\bigstar}$

Resultant resistance

$\orange{\bigstar}$  Knowledge required  $\green{\bigstar}$

If resistor's are connected are in series ,

$\bf R_{eq}=R_1+R_2+R_3+...$

If "n" equal resistor's are connected in series ,

$\implies \bf R_{eq}=R+R+R+...\\\\\bf \implies \pink{R_{eq}=nR\ \; \bigstar}$

$\orange{\bigstar}$  Solution  $\green{\bigstar}$

Here three resistors of equal resistance 5 Ω  are connected in series ,

$\to \rm R_{eq}=3(5)\ \Omega\\\\\to \bf R_{eq}=15\ \Omega$

So , Combined resistance is equal's to 15 Ω

$\orange{\bigstar}$  Explore More  $\green{\bigstar}$

If resistor's are connected in parallel ,

$\bf \dfrac{1}{R_{eq}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}+...\ \; \pink{\bigstar}$

If n equal resistor's are connected in parallel ,

$\bf R_{eq}= \dfrac{R}{n}\ \; \pink {\bigstar}$

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Answer 2

$\mathcal{\gray{\underbrace{\blue{GIVEN:-}}}}$

• Three resistors of resistance 5Ω each are connected in series .

$\mathcal{\gray{\underbrace{\blue{TO\: FIND:-}}}}$

• The combined resistance .

$\mathcal{\gray{\underbrace{\blue{SOLUTION:-}}}}$

⚡ If n number of resistance are connected in series and their resistance are equal to each other then the combined/equivalent resistance is,

$\orange\bigstar\:\rm{\pink{\boxed{\purple{R_{eq}\:=\:n\:R}}}}$

⚡ If n number of resistance are connected in parallel and their resistance are equal to each other then the combined/equivalent resistance is,

$\orange\bigstar\:\rm{\pink{\boxed{\purple{R_{eq}\:=\:\dfrac{R}{n}\:}}}}$

Where,

• n = number of resistor .

• R = resistance of resistor .

Here, series combination is given .

Where,

• n = 3

• R = 5Ω

$\rm{\implies\:R_{eq}\:=\:3\times{5}\:}$

$\rm{\green{\implies\:R_{eq}\:=\:15\Omega\:}}$

$\rm\pink{\therefore}$ The combined resistance will be equal to “15Ω” .

MORE INFO :-

Equivalent Resistance :-

For Series Combination :-

$\blue\bigstar\:\rm{\pink{\boxed{\green{R_{eq}\:=\:R_1\:+\:R_2\:+\:R_3\:+\:......\:+\:R_n\:}}}}$

For Parallel combination :-

$\blue\bigstar\:\rm{\pink{\boxed{\green{\dfrac{1}{R_{eq}}\:=\:\dfrac{1}{R_1}\:+\:\dfrac{1}{R_2}\:+\:\dfrac{1}{R_3}\:+\:......\:+\:\dfrac{1}{R_n}\:}}}}$