Question

Two resistors R₁ = 8.3 Ω and R₂ = 1.6 Ω are connected in parallel and a potential difference of Delta V = 12.0 V is imposed across them. Find the currents I₁ and I₂, and the current through the battery, I. Find the equivalent resistance of the circuit.

Answer 1

The currents I₁ and I₂ through resistors R₁ and R₂ are approximately 1.45 A and 7.5 A, respectively, and the total current I through the battery is 8.95 A. The equivalent resistance of the parallel combination of resistors is approximately 1.47 Ω.

Step-by-step explanation:

When two resistors R₁ = 8.3 Ω and R₂ = 1.6 Ω are connected in parallel and subjected to a potential difference of ΔV = 12.0 V, we can find the individual currents using Ohm's Law, I = V/R.

The current through R₁ (I₁) is:

I₁ = ΔV / R₁ = 12.0 V / 8.3 Ω = 1.4458 A (approximately 1.45 A)

The current through R₂ (I₂) is:

I₂ = ΔV / R₂ = 12.0 V / 1.6 Ω = 7.5 A

The total current through the battery (I) is the sum of I₁ and I₂:

I = I₁ + I₂ = 1.45 A + 7.5 A = 8.95 A

To find the equivalent resistance (Rₒ₀₁) of the parallel combination of resistors, we use the formula:

1/Rₒ₀₁ = 1/R₁ + 1/R₂

Rₒ₀₁ = 1 / (1/8.3 Ω + 1/1.6 Ω) ≈ 1.47 Ω

The equivalent resistance of the circuit is therefore approximately 1.47 Ω.