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.
Answer:
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
