Question

three resistance of 10, 15 and 20ohms are connected in parallel .find the effective resistance
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Answer 1

Answer:

13/60 ohms

Step-by-step explanation:

since effective resistance in parallel is

1/R1 + 1/R2 + 1/R3 ......

1/10 + 1/15 + 1/20 = 13/60

Answer 2

★GIVEN★

Three resistance of 10, 15 and 20 ohms are connected in parallel.

★To Find★

The effective resistance.

★SOLUTION★

We know that,

Effective resistance in parallel circuit is,

$\large{\pink{\underline{\boxed{\sf{\dfrac{1}{R_{p}}=\dfrac{1}{R_{1}}+\dfrac{1}{R_{2}}+\dfrac{1}{R_{3}}+\:so\:on....}}}}}$

Three resistances = 10 ohm, 15 ohm, 20 ohm.

• $\large{\sf{Let\:R_{1}\:be\:10\:ohm.}}$
• $\large{\sf{Let\:R_{2}\:be\:15\:ohm.}}$
• $\large{\sf{Let\:R_{3}\:be\:20\:ohm.}}$

Putting the values,

$\large\implies{\sf{\dfrac{1}{R_{p}}=\dfrac{1}{R_{1}}+\dfrac{1}{R_{2}}+\dfrac{1}{R_{3}}}}$

$\large\implies{\sf{\dfrac{1}{R_{p}}=\dfrac{1}{10}+\dfrac{1}{15}+\dfrac{1}{20}}}$

LCM of 10, 15 and 20 is 60.

$\large\implies{\sf{\dfrac{1}{R_{p}}=\dfrac{6+4+3}{60}}}$

$\large\implies{\sf{\dfrac{1}{R_{p}}=\dfrac{13}{60}}}$

$\large\implies{\sf{R=\dfrac{60}{13}}}$

$\large\therefore\boxed{\sf{\pink{R=6.41\:ohm.}}}$

$\large{\pink{\underline{\boxed{\therefore{\bf{Effective\:Resistance\:=6.41\:ohm.}}}}}}$