Parallel Circuits and Total Resistance

Which of the following equations correctly represents the total resistance (RT) for three resistors (R1, R2, R3) connected in parallel?

• 1/RT = 1/R1 + 1/R2 + 1/R3

• RT = R1 + R2 + R3

• RT = R1 × R2 × R3

• RT = (R1 + R2 + R3)/3

If R1 = 2 Ω, R2 = 4 Ω, and R3 = 4 Ω are connected in parallel, what is the total resistance RT?

• 1 Ω

• 2 Ω

• 4 Ω

• 10 Ω

Explain why the total resistance in a parallel circuit is always less than the smallest individual resistor.

• Because adding more paths allows more current to flow, reducing overall resistance.

• Because the resistors cancel each other out.

• Because the voltage increases in parallel circuits.

• Because the resistors are not connected to a power source.

When calculating the total resistance of the parallel circuit, what is the lowest common denominator used to add the fractions 1/9, 1/12, and 1/18?

• 18

• 36

• 12

• 9

After finding the lowest common denominator, what is the sum of the numerators when adding 1/9, 1/12, and 1/18 to find 1/Rₜ?

• 7

• 8

• 9

• 10

Using the formula for parallel resistance, explain why the total resistance of a parallel circuit is always less than the smallest individual resistor in the circuit.

• Because the resistors are added directly.

• Because the reciprocal of the total resistance is the sum of the reciprocals of the individual resistances.

• Because the voltage is divided among the resistors.

• Because the current is the same through each resistor.

Why is the total resistance of a circuit important?

• It determines the amount of current that will flow in the circuit.

• It determines the voltage of the circuit.

• It determines the power source of the circuit.

• It determines the length of the wires in the circuit.

Given the equation R_T = 36/9, explain the process used to find the total resistance of the circuit.

• By dividing 36 by 9 to get the total resistance.

• By multiplying 36 by 9 to get the total resistance.

• By adding 36 and 9 to get the total resistance.

• By subtracting 9 from 36 to get the total resistance.

Given three resistors in parallel with values R₁ = 45Ω, R₂ = 90Ω, and R₃ = 30Ω, which equation correctly represents the formula to calculate the total resistance (Rₜ) of the parallel circuit?

• 1/Rₜ = 1/R₁ + 1/R₂ + 1/R₃

• Rₜ = R₁ + R₂ + R₃

• Rₜ = R₁ × R₂ × R₃

• 1/Rₜ = R₁ + R₂ + R₃

• 15Ω

• 12Ω

• 6Ω

• 9Ω