Question

R1=6ohm,R2=5ohm,R3=15ohm are in parallel combination. find equivalent resistance​

Answer 1

R1= 6 ohm
R2= 5ohm
R3= 15ohm

See attachment for answer

Answer 2

Given :-

• $\displaystyle\sf R_1$ = 6Ω
• $\displaystyle\sf R_2$ = 5Ω
• $\displaystyle\sf R_3$ = 15Ω

To Find :-

• The equivalent Resistance?

Solution :-

We know that the equivalent Resistance of a parallel combination is given by,

$\displaystyle\underline{\boxed{\sf\dfrac{1}{R_{net}} = \dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}\dots +\dfrac{1}{R_n}}}$

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$\underline{\bigstar\:\textsf{According to the given Question :}}$

$\displaystyle\sf \dashrightarrow \dfrac{1}{R_{net}} = \dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}\dots +\dfrac{1}{R_n}$

$\displaystyle\sf \dashrightarrow \dfrac{1}{R_{net}} = \dfrac{1}{6}+\dfrac{1}{5}+\dfrac{1}{15}$

$\displaystyle\sf \dashrightarrow \dfrac{1}{R_{net}} = \dfrac{1}{6}\times \dfrac{5}{5} +\dfrac{1}{5}\times \dfrac{6}{6} +\dfrac{1}{15}\times \dfrac{2}{2}$

$\displaystyle\sf \dashrightarrow \dfrac{1}{R_{net}} = \dfrac{5}{30}+\dfrac{6}{30}+\dfrac{2}{30}$

$\displaystyle\sf \dashrightarrow \dfrac{1}{R_{net}} = \dfrac{5+6+2}{30}$

$\displaystyle\sf \dashrightarrow \dfrac{1}{R_{net}} = \dfrac{13}{30}$

$\displaystyle\sf \dashrightarrow R_{net} = \dfrac{30}{13}$

$\displaystyle\sf \dashrightarrow \underline{\boxed{\sf R_{net} = 2.3 \ \Omega}}$

$\displaystyle\therefore\: \underline{\sf Resistance \ across \ the \ Circuit \ will \ be \ 2.3 \Omega}$

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