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