Final answer:
To calculate the resistance across terminals a-b, combine the parallel resistors R₂ and R₃, then add this to the series resistor R₁ to find the total resistance. Apply principles like Ohm's law to confirm the correct reduction.
Step-by-step explanation:
To find the resistance across terminals a-b (rab) by reducing the circuit to a single resistor, we need to follow a strategy. First, we look at the resistors R₂ and R₃ which are in parallel and calculate their combined resistance Rp using the formula for resistors in parallel.
Rp = (R₂ * R₃) / (R₂ + R₃)
Given that R₂ = 6.00 Ω and R₃ = 13.02 Ω, the combined parallel resistance can be calculated accordingly. After finding Rp, we then add this to the resistance of R₁ to find the total equivalent resistance across terminals a-b, as they are in series.
Rtot = R₁ + Rp
Since R₁ is given as 1.00 Ω, the total resistance can easily be calculated.
Finally, we apply Ohm's law and any other necessary physical principles to find the current, voltage drop in each resistor, and the power dissipated by each, ensuring that power output of the source equals the total power dissipated which confirms the correct reduction of the circuit into its single resistor equivalent.