18.Three resistors 5 ohm ,10 ohm , 30 ohm are connected in parallel with 12 V battery. Calculate
a.Current through each resistor
b. Total current in the circuit
c. The total circuit resistance
Answers
Given :
Three resistors are connected in parallel
- R₁ = 5Ω
- R₂ = 10Ω
- R₃ = 30Ω
Potential difference, V = 12V.
To find :
(a) Current through each resistor
(b) The total circuit resistance
(b) Total current in the circuit
Solution :
(a) using ohm's law, .i.e.,
At constant temperature, the current flowing through a conductor is directly proportional to the potential difference across its ends.
In order words,
- V = R × I
where,
V denotes potential difference.
R denotes resistance.
I denotes current.
Current passing through R₁
➠ V = R₁ × I₁
➠ 12 = 5 × I₁
➠ 12/5 = I₁
➠ l₁ = 2.4A
Similarly,
Current passing through R₂
➠ V = R₂ × I₂
➠ 12 = 10 × I₂
➠ 12/10 = I₂
➠ I₂ = 1.2A
Current passing through R₃
➠ V = R₃ × I₃
➠ 12 = 30 × I₃
➠ 12/30 = I₃
➠ I₃ = 0.4
(b) Equivalent resistance of the circuit is given by,
➠ 1/R = 1/R₁ + 1/R₂ + 1/R₃
➠ 1/R = 1/5 + 1/10 + 1/30
➠ 1/R = (6 + 3 + 1)/30
➠ 1/R = 10/30
➠ R = 3Ω
thus, total resistance of the circuit is 3Ω
(c) Total current in the circuit,
using ohm's law,
➠ V = RI
➠ 12 = (3)(I)
➠ 12/3 = I
➠ I = 4A
thus,total current flowing through the circuit is 4A.
Remember !
SI unit of resistance is ohms (Ω)
SI unit of current is ampere (A)
Current passing through R₁
➠ V = R₁ × I₁
➠ 12 = 5 × I₁
➠ 12/5 = I₁
➠ l₁ = 2.4A
Similarly,
Current passing through R₂
➠ V = R₂ × I₂
➠ 12 = 10 × I₂
➠ 12/10 = I₂
➠ I₂ = 1.2A
Current passing through R₃
➠ V = R₃ × I₃
➠ 12 = 30 × I₃
➠ 12/30 = I₃
➠ I₃ = 0.4
(b) Equivalent resistance of the circuit is given by,
➠ 1/R = 1/R₁ + 1/R₂ + 1/R₃
➠ 1/R = 1/5 + 1/10 + 1/30
➠ 1/R = (6 + 3 + 1)/30
➠ 1/R = 10/30
➠ R = 3Ω
thus, total resistance of the circuit is 3Ω
(c) Total current in the circuit,
using ohm's law,
➠ V = RI
➠ 12 = (3)(I)
➠ 12/3 = I
➠ I = 4A{.}.
thus,total current flowing through the circuit is 4A. Ans.