Question

Find the equivalent resistance of three resistors of 5r, 10r and 30r connected in parallel.

Answer 1

Answer :-

Given :-

• $\sf R_1 = 5r$
• $\sf R_2 = 10r$
• $\sf R_3 = 30r$

To Find :-

• Equivalent resistance

Solution :-

For the parallel combination :-

$\implies\sf \dfrac{1}{R_{eq}} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3}$

Substituting the values -

$\implies\sf \dfrac{1}{r_{eq}} = \dfrac{1}{5r} + \dfrac{1}{10r} + \dfrac{1}{30r}$

$\implies\sf \dfrac{1}{r_{eq}} = \dfrac{6}{30r} + \dfrac{3}{10r} + \dfrac{1}{30r}$

$\implies\sf \dfrac{1}{r_{eq}} = \dfrac{6 + 3 + 1}{30r}$

$\implies\sf \dfrac{1}{r_{eq}} = \dfrac{10}{30r}$

$\implies\sf \dfrac{1}{r_{eq}} = \dfrac{1}{3r}$

$\implies\sf r_{eq} = 3r$

So, the equivalent resistance of three resistors of 5r, 10r and 30r connected in parallel is 3r.

Answer 2

✪ Given :-

$\: \: \: \: \: \: \: ➵ \: R1 = 5r$

$\: \: \: \: \: \: \: ➵R2 \: = 10r$

$\: \: \: \: \: \: \: ➵R3 \: = 30r$

✪ To Find :-

☞ Equivalent Resistance

✪ Solution:-

For Parallel Combination :-

$➠ \: \frac{1}{Req} = \frac{1}{R1} + \frac{1}{R2} + \frac{1}{ R3}$

For Substituting the value :-

$</p><p></p><p>➠ \: \sf \dfrac{1}{r_{eq}} = \dfrac{1}{5r} + \dfrac{1}{10r} + \dfrac{1}{30r}</p><p></p><p>$

$</p><p></p><p>➠ \: \sf \dfrac{1}{r_{eq}} = \dfrac{6}{30r} + \dfrac{3}{10r} + \dfrac{1}{30r}</p><p></p><p>$

$</p><p></p><p></p><p>➠ \: \sf \dfrac{1}{r_{eq}} = \frac{6 + 3 + 1}{30r} </p><p></p><p></p><p></p><p>$

$➠ \frac{1}{</p><p>req</p><p>} = \frac{10}{30r}$

$➠ \frac{1}{</p><p>r eq</p><p>} = \frac{1}{3r}$

$➠req = 3r$

Therefore ,The Equivalent of three resistors of 5r ,10r ,and 30r Connected in Parallel is 3r