Question

three resistors of 6ohm each are joined in parallel with 12volt battery .calculate the total resistence and current through each resistors.​

Answer 1

Answer :

• Total resistance in the circuit, Rₙ = 2 Ω
• Current in each resistor, I = 2 A

Explanation :

Given :

• Resistance in the three resistors, R₁ = R₂ = R₃ = 6 Ω.
• Voltage in the circuit, V = 12 V

To find :

• Total resistance in the circuit, Rₙ = ?
• Current in each resistor, I = ?

Knowledge required :

• Formula for total resistance in a parallel circuit :

⠀⠀⠀⠀⠀⠀⠀⠀⠀1/Rₑ = 1/R₁ + 1/R₂ + 1/R₃ + ... + 1/Rₙ⠀

[Where : Rₑ = Equivalent resistance in the circuit, R = Resistance in the resistors]

• Ohm's law :

⠀⠀⠀⠀⠀⠀⠀⠀⠀V = IR⠀

[Where : V = Potential difference, I = Current, R = Resistance]

Solution :

To find the equivalent resistance in the circuit :

⠀By using the formula for equivalent resistance in a parallel circuit and substituting the values in it, we get :

⠀⠀=> 1/Rₑ = 1/R₁ + R₂ + 1/R₃

⠀⠀=> 1/Rₑ = 1/6 + 1/6 + 1/6

⠀⠀=> 1/Rₑ = (1 + 1 + 1)/6

⠀⠀=> 1/Rₑ = 3/6

⠀⠀=> Rₑ = 6/3

⠀⠀=> Rₑ = 2

⠀⠀⠀⠀⠀∴ Rₑ = 2 Ω

Hence the equivalent resistance in the circuit is 2 Ω.

To find the current in the resistor, R₁ = R₂ = R₃ :

⠀By using the ohm's law and Substituting the value in it, we get :

⠀⠀=> V = IR

⠀⠀=> 12 = I × 6

⠀⠀=> 12/6 = I

⠀⠀=> 2 = I

⠀⠀⠀⠀⠀∴ I = 2 A

Hence the current flowing in each resistor is 2 A.