In a parallel circuit, the equivalent resistance is always less than the smallest resistor.

In a parallel circuit, the equivalent resistance is always less than the smallest resistor.

• A. True
• B. False
• C. Sometimes
• D. Not Applicable

Answer: (A)

In parallel, adding more paths for current increases the total conductance while the voltage across each path stays the same. This means the overall resistance subtracts from the individual values. The relationship 1/Req = sum(1/Ri) shows why: each new finite resistor adds a positive term to the sum, making 1/Req larger and thus Req smaller than the smallest individual resistor. For example, 4 ohms in parallel with 6 ohms gives Req = (4×6)/(4+6) = 2.4 ohms, which is less than both resistors. So, in a typical parallel network with more than one finite resistor, the equivalent resistance is indeed less than the smallest resistor.

In parallel, adding more paths for current increases the total conductance while the voltage across each path stays the same. This means the overall resistance subtracts from the individual values. The relationship 1/Req = sum(1/Ri) shows why: each new finite resistor adds a positive term to the sum, making 1/Req larger and thus Req smaller than the smallest individual resistor. For example, 4 ohms in parallel with 6 ohms gives Req = (4×6)/(4+6) = 2.4 ohms, which is less than both resistors. So, in a typical parallel network with more than one finite resistor, the equivalent resistance is indeed less than the smallest resistor.