Parallel Resistors Yield Lower Total Resistance

Steps:

• Identify configuration: Two resistors r and R in parallel, as series would sum to r + R.
• Recall formula: Combined resistance = (r * R) / (r + R).
• Assume r < R: Equivalent resistance is always less than the smaller resistor r.
• Verify: For example, if r = 1Ω and R = 2Ω, combined = (1*2)/(1+2) = 2/3Ω < 1Ω.

Why D is correct:

• Parallel formula (rR)/(r+R) is less than the smaller resistance, per Ohm's law for parallel circuits.

Why the others are wrong:

• A: Equals r + R only in series, not parallel.
• B: Parallel value is below both, not between.
• C: Parallel is always less than r + R.

Final answer: D