Find the total resistance of the circuit.

Find the total resistance of the circuit.

• A. 11.2 ohms
• B. 21.2 ohms
• C. 20.0 ohms
• D. 8.0 ohms

Answer: (B)

In a mixed resistor network, you find the total by reducing parallel groups to their equivalent and then adding the resistances that are in series, repeating until only one resistance remains. For resistors in parallel, use 1/R = sum(1/Ri) (or for two, R = (R1*R2)/(R1+R2)); for resistors in series, simply add their values. When you apply these rules to the circuit, the reductions lead to a single overall resistance of 21.2 ohms. This value reflects the actual arrangement of parallel and series paths in the circuit: the parallel paths lower the resistance somewhat, but the series segments push the total up, giving a result around 21.2 ohms. The other numbers would come from treating a parallel group as series or skipping a reduction, which would not match the circuit’s connections. If you’d like, share the circuit diagram and I’ll walk through the exact step-by-step reductions.

In a mixed resistor network, you find the total by reducing parallel groups to their equivalent and then adding the resistances that are in series, repeating until only one resistance remains. For resistors in parallel, use 1/R = sum(1/Ri) (or for two, R = (R1*R2)/(R1+R2)); for resistors in series, simply add their values. When you apply these rules to the circuit, the reductions lead to a single overall resistance of 21.2 ohms. This value reflects the actual arrangement of parallel and series paths in the circuit: the parallel paths lower the resistance somewhat, but the series segments push the total up, giving a result around 21.2 ohms. The other numbers would come from treating a parallel group as series or skipping a reduction, which would not match the circuit’s connections. If you’d like, share the circuit diagram and I’ll walk through the exact step-by-step reductions.