Final answer:
To find the equivalent resistance between nodes a and b, calculate the parallel resistance of R₂ and R₃ first, then add it to R₁ to get the total resistance.
Step-by-step explanation:
To determine the equivalent resistance between nodes a and b, we must consider the arrangement of resistors in the circuit. Resistors R₂ and R₃ are connected in parallel, after which their combined resistance is in series with R₁. The formula for calculating equivalent resistance in parallel is 1/Rp = 1/R₂ + 1/R₃, where Rp represents the combined resistance of resistors in parallel. Once Rp is determined, the total equivalent resistance (Rtot) of the circuit is simply R₁ plus Rp, denoted by the formula Rtot = R₁ + Rp. Remember that R₁, R₂, and R₃ must be in the same unit before performing any calculations.
Additionally, students can calculate the equivalent resistance of resistors connected in both series and parallel by applying the respective formulae for each configuration. In series, the resistances add up directly, whereas in parallel, the reciprocals of the resistances add up, and the reciprocal of the sum gives the combined resistance.