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)