In the Circuit Diagram Given Below, Three Resistors R1, R2, and R3 of 5 ω, 10 ω and 30 ω, Respectively Are Connected as Shown - Science

In the circuit diagram given below, three resistors R1, R2, and R3 of 5 Ω, 10 Ω and 30 Ω, respectively are connected as shown

Calculate:
(a) current through each resistor.

(b) total current in the circuit.

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Solution

(a) Let I₁, I₂ and I₃ be the current flowing through the resistors of 5 Ω, 100 Ω and 30 Ω, respectively.
According to Ohm's law, V = IR
Here, V = 12 V and R = 5 Ω
I = V/R
I₁ = 12/5 = 2.4 A
I₂ = 12/10 = 1.2 A
I₃ = 12/30 = 0.4 A

(b) Total current through the circuit, I = I₁ + I₂ + I₃
= 2.4 A + 1.2 A + 0.4 A
= 4 A

(c) The resistors of 5 Ω, 100 Ω and 30 Ω are connected in parallel. Therefore, the net resistance will be:
1/ R = 1/R₁ + 1/R₂ + 1/R₃
1/R = (1/5) + (1/10) + (1/30)
1/R = (6 + 3 +1)/30
I/R = 10/30
R = 3 Ω