Question

In the circuit given below, identify the correct relation between the currents flowing through the 2 Ω, 3 Ω, and 5 Ω resistors:

पर्याय

• current through 2 Ω > current through 3 Ω

• current through 5 Ω < current through 3 Ω

• current through 2 Ω = current through 5 Ω

• current through 5 Ω > current through 3 Ω

Answer 1

Current through 2 Ω = current through 5 Ω

Explanation:

The circuit has a 12 V DC source connected to two parallel branches.

Branch 1 contains two resistors in series: 3 Ω and 2 Ω.

Total resistance of Branch 1 (R₁) = 3 Ω + 2 Ω = 5 Ω

Branch 2 contains one resistor of 5 Ω.

Total resistance of Branch 2 (R₂) = 5 Ω

In a parallel circuit, the voltage across each parallel branch is the same as the source voltage (12 V).

I₁ = `V/R_1`

= `12/5`

= 2.4 A

I₂ = `V/R_2`

= `12/5`

= 2.4 A

The total resistance of the series combination (3 Ω + 2 Ω) is 5 Ω. Since this branch is in parallel with the single 5 Ω resistor branch, and both branches have equal total resistance, the current divides equally between them according to Ohm’s law `(I = V/R)`. Thus, the currents are equal.