Question

Find the equivalent resistance when 5 Ω, 10 Ω, and 30 Ω resistors are connected in parallel

Answer 1

Answer:

effective resistance is 3 Ω

Step-by-step explanation:

Let R1 = 5 Ω , R2 =10 Ω, R3 = 30 Ω

For parallel combination, effective resistance Rp is

1/ Rp = 1/R1 + 1/R2 + 1/R3  

1/Rp = 1/ 5 + 1/10 + 1/ 30 = ( 6 + 3 + 1) / 30 = 10/ 30 = 1/3

Rp = 3 Ω

Hence, effective resistance is 3 Ω

Answer 2

Given :-

• 5Ω , 10 Ω, and 30 Ω resistors are connected in parallel.

To Find :-

• Equivalent resistance.

Solution :-

Equivalent resistance :-

$:\implies\:\sf{\dfrac{1}{R_1} +\dfrac{1}{R_2} + \dfrac{1}{R_3} }$

Here,

$\longrightarrow\:\:\sf{R_1=5 \Omega}$

$\longrightarrow\:\:\sf{R_2 =10\Omega }$

$\longrightarrow\:\:\sf{R_3 = 30\Omega}$

$:\implies\:\sf{ \dfrac{1}{R_p} = \dfrac{1}{5}+\dfrac{1}{10} +\dfrac{1}{30} }$

$:\implies\:\sf{ \dfrac{1}{R_p} = \dfrac{(6+3+1)}{30} }$

$:\implies\:\sf{\dfrac{1}{R_p} = \dfrac{10}{30} }$

$:\implies\: \sf{ \dfrac{1}{R_p} = \dfrac{1}{3} }$

$\sf:\implies \underline{\boxed{\pink{\mathfrak{\dfrac{1}{R_p} = 3\Omega}}}}$

∴ Equivalent resistance = 3Ω.