Question

Find the equivalent resistance for 20ohm 15ohm and 20ohm parallel conecetion

Answer 1

GIVEN :-

1. Three resistors of 20Ω , 15Ω , 20Ω.

TO FIND :-

1. The equivalent resistance.

SOLUTION :-

Let R₁ be 20Ω R₂ be 15Ω R₃ be 20Ω.

Now as we know that , when the resistors are connected in parallel combination then their equivalent resistance is given by,

$\\ : \implies \displaystyle \sf \: \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ... + \frac{1}{R_n}$

$: \implies \displaystyle \sf \: \frac{1}{R_{eq}} = \frac{1}{20} + \frac{1}{15} + \frac{1}{20}$

$: \implies \displaystyle \sf \: \frac{1}{R_{eq}} = \frac{3 + 4 + 3}{60}$

$: \implies \displaystyle \sf \: \frac{1}{R_{eq}} = \frac{10}{60}$

$: \implies \displaystyle \sf \: \frac{1}{R_{eq}} = \frac{1}{6}$

$: \implies \displaystyle \underline{ \boxed{\sf \bold{ \: {R_{eq}} = 6 \: \Omega}}}$

Answer 2

Given

⠀

$\begin{lgathered}\begin{lgathered}\begin{lgathered}\tt {\pink{Three\: resistors}}\begin{cases} \sf{\green{R_1 = 20 Ω}}\\ \sf{\blue{R_2 = 15 Ω}}\\ \sf{\orange{R_3 = 20 Ω}}\end{cases}\end{lgathered} \:\end{lgathered}\end{lgathered}$

⠀

To find

• Equivalent resistance.

Solution

★ We know that, in parallel connection

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

» Putting the values

$\implies{\dfrac{1}{R_{eq}} = \dfrac{1}{20} + \dfrac{1}{15} + \dfrac{1}{20}}$

⠀

$\implies{\dfrac{1}{R_{eq}} = \dfrac{3 + 4 + 3}{60}}$

⠀

$\implies{\dfrac{1}{R_{eq}} = \dfrac{10}{60}}$

⠀

$\implies{\dfrac{1}{R_{eq}} = \dfrac{1}{6}}$

⠀

$\implies{R_{eq} = 6Ω}$

⠀

Hence, the equivalent resistance is 6Ω.