2. A parallel circuit has 3 resistors each on different paths connected to a 120 V potential difference. Do the resistors have resistances of 5.0 Ω, 7.5 Ω, and 9.8 Ω?

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

A parallel circuit has 3 resistors each on different paths connected to a 120 V potential difference. Do the resistors have resistances of 5.0 Ω, 7.5 Ω, and 9.8 Ω?

Find current, voltage, and power of each resistor and overall circuit.

V₁ = 120 V, V₂ = 120 V, V₃ = 120 V, Vnet = 120 V

I₁ = 24, I₂ = 16, I₃ = 12.24, Inet = 52.24 A

P₁ = 2880 W, P₂ = 1920 W, P₃ = 1469 W, Pnet = 6269 W

Req = 2.30 Ω

Explanation:

Three resistors are connected in parallel with 120 V potential difference.

R₁ = 5.0 Ω

R₂ = 7.5 Ω

R₃ = 9.8 Ω

The voltage across each resistor would be same since they are connected in parallel.

V₁ = 120 V

V₂ = 120 V

V₃ = 120 V

The overall voltage across the circuit would also be same

Vnet = 120 V

The current through each resistor is given by

I = V/R

I₁ = V/R₁ = 120/5.0 = 24 A

I₂ = V/R₂ = 120/7.5 = 16 A

I₃ = V/R₃ = 120/9.8 = 12.24 A

The overall voltage in the circuit is

Inet = I₁ + I₂ + I₃ = 24 + 16 + 12.24 = 52.24 A

The power dissipated across each resistor is given by

P = VI

P₁ = VI₁ = 120*24 = 2880 W

P₂ = VI₂ = 120*16 = 1920 W

P₃ = VI₃ = 120*12.24 = 1469 W

The overall power in the circuit is

Pnet = P₁ + P₂ + P₃ = 2880 + 1920 + 1469 = 6269 W

The net equivalent resistance of the circuit is

1/Req = 1/R₁ + 1/R₂ + 1/R₃

1/Req = 1/5.0 + 1/7.5 + 1/9.8

1/Req = 0.4353

Req = 1/0.4353

Req = 2.30 Ω

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