Question

three resistance 2ohm,4ohm and 8ohm are connected in parallel.if total current from battery is8 amp then find total potential of battery and current through each resistance.

Answer 1

Answer:

$\bigstar{\bold{Potential\:difference=9.12\:V}}$

$\bigstar{\bold{Current\:through\:first\:resistor=4.56\:A}}$

$\bigstar{\bold{Current\:through\:second\:resistor=2.28\:A}}$

$\bigstar{\bold{Current\:through\:third\:resistor=1.14\:A}}$

Explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• Resistance(R₁) = 2 Ω
• Resistance (R₂) = 4 Ω
• Resistance (R₃) = 8 Ω
• Current (I) = 8 A

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Potential difference (V)
• Current through each resistance

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ First we have to find the effective resistance of the resistors.

→ The effective resistance when resistors are given in parallel is given by,

   $\dfrac{1}{R}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}$

→ Substituting the datas we get,

  $\dfrac{1}{R}=\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}$

→ Simplifying it,

  $\dfrac{1}{R}=\dfrac{4}{8}+\dfrac{2}{8}+\dfrac{1}{8}$

 $\dfrac{1}{R}=\dfrac{7}{8}$

R = 8/7

R = 1.14 Ω

→ Hence effective resistance is 1.14 Ω

→ We know that by Ohm's law

  V = I R

→ Substituting the datas,

   V = 8 × 1.14

   V = 9.12 V

$\boxed{\bold{Potential\:difference=9.12\:V}}$

Current through first resistor:

→ By Ohm's law,

  I₁ = V/R₁

→ Substituting datas

  I₁ = 9.12/2

  I₁ = 4.56 A

$\boxed{\bold{Current\:through\:first\:resistor=4.56\:A}}$

Current through second resistor:

→ I₂ = V/R₂

→ Substituting datas,

  I₂ = 9.12/4

  I₂ = 2.28 A

$\boxed{\bold{Current\:through\:second\:resistor=2.28\:A}}$

Current through third resistor:

→ I₃ = V/R₃

→ Substitute the datas,

   I₃ = 9.12/8

   I₃ = 1.14 A

$\boxed{\bold{Current\:through\:third\:resistor=1.14\:A}}$