Question

the resultant resistance of a circuit where 10ohm, 20ohm, 30ohm, and 40ohm, are connected in parallel

Answer 1

Answer:

Rp= 5.45 ohm

Explanation:

1/Rp = 1/R1 + 1/R2 + 1/R3

1/Rp = 1/10 + 1/20 + 1/30

1/Rp = 0.1833

Rp= 1/ 0.18333

Rp = 5.45 Ohm

Answer 2

the resultant resistance of a circuit where 10ohm, 20ohm, 30ohm, and 40ohm, are connected in parallel

effective resistance for parallel combination :

$\sf{\dfrac{1}{Req} = \dfrac{1}{R1} + \dfrac{1}{R2} + \dfrac{1}{R3} + \dfrac{1}{R4}}$

• let R1 = 10 ohm

• R2 = 20 ohm

• R3 = 30 ohm

• R4 = 40 ohm

$\sf\longrightarrow{\dfrac{1}{Req} = \dfrac{1}{10} + \dfrac{1}{20} + \dfrac{1}{30} + \dfrac{1}{40}}$

$\sf\longrightarrow{\dfrac{1}{Req} = \dfrac{1\times 12}{10\times 12} + \dfrac{1\times 6}{20\times 6} + \dfrac{1\times 4}{30\times 4} + \dfrac{1\times 3}{40\times 3}}$

$\sf\longrightarrow{\dfrac{1}{Req} = \dfrac{1\times 12}{10\times 12} + \dfrac{1\times 6}{20\times 6} + \dfrac{1\times 4}{30\times 4} + \dfrac{1\times 3}{40\times 3}}$

$\sf\longrightarrow\sf{\dfrac{1}{Req} = \dfrac{ 12}{120} + \dfrac{ 6}{120} + \dfrac{4}{120} + \dfrac{3}{120}}$

$\sf\longrightarrow\sf{\dfrac{1}{Req} = \dfrac{ 12 + 6 + 4 + 3}{120}}$

$\sf\longrightarrow{\dfrac{1}{Req} = \dfrac{ 18 + 7}{120}}$

$\sf\longrightarrow{\dfrac{1}{Req} = \dfrac{ 25}{120}}$

$\sf\longrightarrow{Req = \dfrac{120}{25}}$

$\sf\longrightarrow{Req = 4.8 ohm }$