Final answer:
The equivalent resistance of a circuit with four resistors connected in parallel with a 12-volt battery can be calculated by summing the reciprocals of each resistance and then taking the reciprocal of that sum, resulting in approximately 56.51 Ω.
Step-by-step explanation:
The student asked how to calculate the equivalent resistance of a circuit that consists of four resistors (R1 = 150 Ω, R2 = 250 Ω, R3 = 350 Ω, R4 = 450 Ω) connected in parallel with a 12-volt battery. When resistors are connected in parallel, the reciprocal of the total resistance (Requiv) can be found by summing the reciprocals of each individual resistance:
1/Requiv = 1/R1 + 1/R2 + 1/R3 + 1/R4
Plugging in the values:
1/Requiv = 1/150 Ω + 1/250 Ω + 1/350 Ω + 1/450 Ω
1/Requiv = (1/150 + 1/250 + 1/350 + 1/450) Ω-1
To get Requiv, take the reciprocal of the right-hand side of the equation:
Requiv = 1 / (1/150 + 1/250 + 1/350 + 1/450) Ω
After doing the calculations:
Requiv ≈ 56.51 Ω
The equivalent resistance of the circuit is approximately 56.51 Ω.